Anhomaua-Ha pRae KOHKpeTHbIX npHmepOB Ioka3aHO, YTO IIOMeHa 3HePROHOCTeJIa TENIOBOI FOpMbIBNKeHHN3HTPOINHE KaK KOOpDnHaTOI TENIOo6MeHaIIpHBODHT K P4y HapaIOrH3MOB, UHCJO KOToPbIX pactET IO Mepe pacuHInpeHH cΦepb IpnIOJKeHH TepMOHNAMHK. BCKpbITb rHOceOJIOrHueckne KopHN 3THX IapAIOrH3MOB INIpeIIOJKeHa6OJIee O6UAA Mepa KOJINueCTBa XAOTHueCKOTOIBHXeHH, Ha3BAHHa JIA KpatKocTH TepMOHNYJBcOM.I0ka3aHO, KAKero IpnMeHenhe BmecTO 3HTPOINHyCTpaHReTIIpaKTNUeCKN BCE N3BeCTHbIE H O6HApUKeHHbIEABTOPMnAPAIOrH3MbI, BKJIIOUaI npEciKa3aAHNE TENIOBOI CMEPTN BCEJIeHHoI HderpaDAUH N6IOJIOrHuCkNX cnCTem.CdJIan BBiBOi, YTO ZAmeha 3HTPOINNI TepMOHNyJBcOMOTKpbIBaetTIb K paCCHIpeHHIO BO3MOXHOCTeTepMOHNAMHueCKOTO MeToJa IIPN HCCJIeIOBAHH HepaBHOBeCHbIX cHCTeM H HeCTaTHueCKHX IIpoUeCCOB, K CHHTe3y TepMOHNAMHKn C dpyHMn FyHdaMeHTaJIbHBIMN HNCIIHNHHAMH N K 60JIee TjIy6OKOMY IONHMAHHIO MHPOyCTPOINCTBa. ## I. BveeHne IpoIIIO 6OJIeepoIIOJIyTopa cTOLJEHn C ToI IopBI, KaB B eCTeCTBO3HaHHe BOIIIO IOHJrTHne 3HTPOIIHH N IIpHHIIe ee BO3paCTaHnB H HeOBpaTHMbIX IIpoIeCCax [1]. OJHaKo Do cHX IOp He yTHXaIOT CIOpbl O COKPOBeHHOM CMBICJe 3TOI0 IOHJrTHN IO $\phi$ H3NuEcKHX OCHOBaHHx YIOMaHyTORO IIpHHUINIIa [2], IIpHBdIIeRo K yTpate TepMOiINHaMHKOH 6bIIO JcJIaBBI TeOPHN, «YbN BBIOBbI HNKOrJa H HKeM He 6yDyT OIIPOBeprHyTB] [3]. B OBIIIHPHOH HauHyOH H OKIoHOayHNO JInTepeAType eI IOscBraIeHbI COTHN KHn H TBic4uCtATEe, rE 3TH BOIIPOCSb IOcbSyJdeHbI C pa3JIuHbIX TOueK 3peHn [4]. Tem He MeHee Io cHX IOp He IOKa3aHa HcpePbIBaIOHm 6bpa3OM HecocToTReJBHoCTb TeOPHN TEIIIOBOIcmptn BceJIeHHoP. KJIay3Hyca [2] H He ycTaPaeHO «BOIIIOIIee IPoTHBopeUHe TepMOIHAMHKn C 3BOJIIOIIeel [5]. Tem BpemHeM IOHJrTHne 3HTPOIIHH IpePeIarHyIoo rpaHHbI ΦH3IKn I IpOHNKIO B caMbIE cOKPOBeHHbIe 6blaactn YcJIobYeCECKoM MbICJH. HapJyC tEPMOIHAMHueCKoN 3HTPOIINEe P. KJIay3Hyca IIOBHLAcB cTaTHCTNUeCKa, IHΦOpMaIIOHNa, MaTeMaTHueCKa, JINHRBHCtHuCeCKa, INTEJIeKTyAlbHaN T. II. 3HTPOIIHH, YTO eIe 6OJIeocOJIgKHIIO INHTepPiPeTaIHHO 3TOI ROIINKOHO IILOXO IOIDAAHOITcOe HHTYHTNBHOMY BOCIPPNTHIO IOHATNIA. Ha 3TOM foHe ocTaBaJIINcB He3aMeYeHHbIMN IIOIbITKN IOKa3aTb HeaJeKBaTHOCtB IIOHrTH NHTPOIIHN cyIeCTBy IeJa [6]. HApOToHB, CXoJHaN C npapAoKcOM INo6ca H TeOpHei TeIIIOBOm cMePTn CNTyaIINs BO3HNKJa IpaKaTHueCKn B KaJIoB OBJAcTH IIpHIOJKeHNr TepMOINHAMNKH, BKJIIOUaH N3JIyueHHe, HeTeIIIOBbIe H peJIaTHBNCtCKne MaIIHHbI, 6HOJIIOHueCKne ChCTeMbI H CHCTeMbIc OTPiCaTEJBHbIMN a6COJIHOThbIX TeMIIepaTypAMn H DnCKpeTHoH eHeprHei, H T. II. [7]. 3HTPOIIINr CTAJa AaxJIIEcoBOI IYTOI> TepMOINHAMHKN H K03JLOM OTIIuIeHHra 3a JIO6yIO H BCaKyIO> HeO6paTHMoCTb [8]. IeJb 3ToB cTaTbH - IOKa3aTb, HAcKOJIbKO IIJIe3HOm MOKeT 6bITb 3aMeHa 3HTPOIIHH TepMOHMIIyJBcOM KaK 6OJIee aJeKBaTHoH 3KCTeHCHBHOr Mepo TeIIIOBOrO IIBHXeHH. ## II. Heo6xoJMOocTb PepeonpeJeHnIy I3HaHnIa ### 3HTponnnn n3 TepMoDnHaMnKn ПОЯТHE эHTroПИИ B TepMOДиHAMнКе P. KIay3Hyca[1] Hepa3pyBIBHO CB83aHO c erO IpeДCTaBJIeHHem O TeIIIOTe Qn pa6Ote W KaK O DBYx eINHCTBeHNO BO3MOJKBiX CIIOC6bax əHepr0o6MeHa ChCTeMbIC OKpykaHoiSe CpeIoN. 3To CJIeIyET H3 erO 3aIIHcN eOCHOBHOrO 3aKOHa (1- ro NaJa TepMOДиHAMnKN)ВВIDe: $$ \mathrm{d}U=\delta Q-\delta W=\mathrm{T}\,\mathrm{d}S-\mathrm{p}\,\mathrm{d}V, $$ rIe U - BHyTpEHHJEAHepRnCnCTEmbl;8Q,8W-3JIeMeHTapHbIE KOJIHcEcTBA TeIIJa, IIOJIIOIIeHHOrO CnCTEmo, H pa60tBi, COBepHHeHHo eIo; T, S - a6coJIHOthAaTeMIIepaTypa H 3HTpOIIHp; p, V- a6coJIHOthoe DaJIeHHe N o6bEM CNCTEmbl. MekIy TeMIO KJIay3Hnca cyIeCTBOBAJIO npYrOe IIpeIcTaBJIeHHe O TeIIIOTe KaK O HeBecOMOM H HeyHNHTOJKHMbIM $\phi$ IIOHJe, HMeHyEbIM TeIIIOPOJOM. IprN 3TOM TeIIIOTapaccMaTpHBaJIacb B OJHOm pAHy c TaKHMN YBJIeHNM, KaK CBeT, 3JIeKtpHuEcTBO, MaHHeTH3M N T. II., T. e. KaK $\phi$ yHKIIra cocToHnna, a He IpoIecca. TaKoe IOHHMaHHe TeIIIOtBi Do cHX Iop COxpaHHIOcb B KJIaccHueckoTepMOIHHAMKe B IOHATNI TEIIIOeMKocTH cnCTembl[9] H B TeOpHN TEIIIOo6MeHa, KOtOpbl OIIpeJIeTcKa K IpoIeCC o6MeHa MekIy TeJIaMH BHYTrpEHNe TELIOBOJ 3HeprHnei[10]. BoJee TorO, TaKoe IOHHMaHHe OKa3aJIOcb EINHCTBeHHO IIprHMeJIEMbIM N IJIa TepMOIHAMHKn Heo6paTMbIX IpoIeCCOB (THII), OIIepHpyoIe IIOHATHE M BHYTrpEHnX HcTOHKnOB TeIIa[11-14.]a n cam P. KJIay3Hyc IepBOHaJbHo OIIepHPOBaJI IOHATHEM «IOJIHOI TeIIIOtBi TEJa» KaK CUMMbI TEIIIOtBi, IOJBeJHHO H3BHe N BbIeJIINBIIeJcB HByTrpN TeJa B pe3yJbTaTe COBepIeHHN «pa60tBi HnCprEaIHN> DnCCnIaTHBHO XapaKTepa [1]. OJHaKOTaKaI IIOMeHa IIOHrTHe TEPITbI CTaJa 6oJIee 3aMeTHOH C IepExOIOM K H3UyeHHIO OTKpbITbIX CnCTEm, rIe HapAly C TeIIIOOOMeHOM H pa60ToI cyIecTByET IIO KpaIHei Mepe eIe DBaBNa 3HePFOOOMeHa: Maccoo6MeH, XapaKTepH3yOIOIHcRc H3MeHEHem Macsbl cHcTEmbl II pRn HEn3MeHHocTH e e coCTaBA, H nΦfpy3nK-TO BeIeCTBA Ype3 TpaHIIbI CnCTEmbl, XapaKTepH3YIOIIaIcR H3MeHEHem CoCTaBA CnCTEmbl II pRn HEn3MeHHocTH e e Maccbl. IIpn 3tOM Ha TpAHIIe, rIe HMeet MeCto Maccoo6MeH HJIIN DΦfpy3nR, «KJIaCCNHueCKHe IOHHTN T EIIIOBTb I pa60BTb I TEOB CBOI CBICJI» [15]. EIIe 6oJIee IIpo6JIeMHbIM CTAJIIO DeJIeHne 3HePFOOOMeHa HA TeIIIOOOMeH H pa60Ty B CIOJXbIX (IOJIHBapHaHTbIX) CnCTeMax, COBepIIaOIOIHx IOMHMo pa60BTb I paSCIIpeHHN8 Wp= pdV npyrhe BNbI BHeIIHe I pa60BTb Wc (MexAHueckHX, 3JIeKTPnuCeKHx H T. II. cnJI). 3JIeMeHTarHbIE KOJIHueCTBA 3THX BVIOB BVIIeB HBeIIeHHm BeKTopa dWc H3MepeIAIOcb IIPOHN3BeIeHHm BeKTopa pe3yJIbTIpyIOIIe cNIbI F Ha BbI3BaHHoe eIO IpeMeIeHne dro6bKeTa eI pInIOJKeHHa, a cama pa60Tad Wc = dE = Fi·dr; IIpeIcTAbJIa co60I KOJIHueCTBeHHyO Mepy IpoIecca IIpeBpaIIeHHN BHeIIHe N HeOHO (i-) e foPMBI E i B npTuO (j-IO)Ej. TaKaI pa60Ta He 3aBHeJIa O T IyTN IIpoIeCCA, a e e 3JIeMeHTapHOE KOJIHueCTBO dWc JBIAIOCB IIIOHbIM INΦfpeHHuaJIOM.K HeI OTHOCHLIacb H pa60Ta rA3a B IIOTOke -Vdp[16]. 3THBIIbI pa60BTb IpiHIIHaiJIbHO OTJNUaIacb OT pa60BTb BCEtOpOHHeTo pacIIHpENPAIDPDVPpeJDe BCERO HAIIpaBJIeHHOCbIO IIpoIeCCA IIpeMeIeHHN (BeKTopHOI pInpOIOI CBOHX KoopDINHaT R), a TaKZe 3ABHCIMOCbIO OT PyTH (XapaKTepa) IIpoIeCCA (IOCSJeHHe IIOJYePKIBaETcR OOB3HaueHHm e e 3JIeMeHTapHOO KOJIHueCTBA cepW). TaKOrO BVla pa60Ta COBepIIaETcR He TOJbKO IIpN paCINHPEHHH, HO II pRn BBoDE B CNCTeMy BeIeCTBa, ZapJa, HMIIyJIbca H JIO6Oro IIpyrTO IHeP IOHOChTeJI. K Hx YNCJIy cJIeJyET O TheCTN H TEIIIOOOMeH, IIOCKOIbKY OH TaKZe CBZaH C H3MeHEHEM HMIIYlbcxa AOTNHueCKOTO DVBKeHHa YactHI, COCTABJIIOIIIX CHCTeMy. $\mathbf{Y}\mathbf{T}\mathbf{O}\mathbf{6}\mathbf{b}\mathbf{I}$ pa3JIInuAtb IBe 3TH He3aBnCHMBIE KaTeOpHH pa6oT, IeJIecoo6pa3HO Ha3bIBaTb Hx COOTBEcTBeHHO $\langle \mathrm{TEXHNueckHMn}\rangle$ WtH«HeTeXHNueckHMn> W. HeIOHNMaHne TOrO, YTO $\langle \mathrm{pa60Ta}$ pa6oTe po3HB), Io cHX Iop MeIIaet Oco3HaTb, YTO IcTHHHaJr $\langle \mathrm{JINHNN}$ BOIopa3JeJa] IPOxoIHT He MeKJy TeIIOToJ Q n pa6oToJ W, a MeKJy yIIOpaOeHHbIMnWi t H eUYIopraIOueHHbIMn Wi BnIaMn pa6oT KAc KOJIInueCTBeHHbIMn MepaMH IprHIIINIAJBHo pa3JIuHbIX IIpoIeCCOB $\langle \text{三} \mathrm { H e p } 2 \mathrm { o n } -$ pe6paueHna> N «OhepzonepeHocA>[17]. CJIeIyET 3AmETNb, YTO IJIcIIOXbIX CnCTeM, B KOTOp bK IIpOeKaHOT N Te, I dpyTHe IIpoIeCsbI,IOKa3aTeJIbCTB cyIeCTBOBaHHN 3HTPOIIHH KaK KoOpdHaTb TEIIIOo6MeHaIO HactOJIeTO BpeMeHH He cyIueCTByet [18]. IMeetc eOIOHO 6oCToTJIbCTBO, BbHyJdaIOUe BO3BpaHTbC K IOHcKy 6oJIee 6oIIe8 OKeTeHCNBHO Mepbl TeIIOIbTI (eE 3HePFOHOCHTEJI), HeKeJIIN 3HTPOIIH. OHO 3aKJIIOVAeTCB TOM, YTO B MExaHHke, Ha OCHOBE KOtOpOI BO3HKNJIa TepMOHNAMHaKa, BCE IIpoIecCbI cHTaJIHcB 6OpaTHMbIMN (HdyIHMn KaK B IprMOM,TaK H B o6paTHOM HaIIpaBJIeHNN 6e3 KaKHX-JIN6O octaToCHbIX H3MeHeHNN B OKpyJauoIe CpeJe).TakOBoi 6blJa H TeOp TELIOBbIX MaHHN C.KapHo [19], 6a3npyIOIIaIcraHa IpeIIOJKeHHOM Hm MeTOJe IINKIOB. Camo IIHOHTHE IIKJIa IpeIIOJIaIgAJO BO3MOJXHOCTb BO3BpaIeHNA pa6OyeTeJIa TEJIIOBOIM MaIHINbIB HxC0JHOe COCTOHHne, T. e. O6paTHMOCTb IPOHCXODIINX C HMMIIPOIeCCOB, YTO BIOJIHe COOTBeTCTBOBAJIO IpeIcTaBJIeHHO O TEJIIOPOJe KAK HOCHTeJIe TEJIIOBOI $\phi$ opMbI 3HeprHH. IIO-BHNIMOMy, JINIIIb IIIOJHOe KpyIIEHNEIpeIDCTaBJIeHHN O HeyHNUToKHMbIX H HeBecOMbIX $\phi$ IHOJax IOMEIIAO JKIay3NHyCy VBnDEtB 3TO H IpeeyTN K TpaKTOBKe TEJIOTbI JINIIIb KAK KOJInueCTBeHHOmebpI IIpoIecca TEJIIOOOMeHa. Bo3MOJHO, 3TOMy cIIOco6CTBOBaJIO N CBOIcTBO TEJIOTb IpeTeKaTb «CaMOIIPOH3BOJIbHO» JINIIIb B HAIIpaBJIeHHN IIOHJKeHHN TEMpePaTypbI, KOTOPoe 6blIO IOLOKeHO HMB OCHOBAHne erO $\phi$ opMyIInpOBKn 2-TO NaHajIA TePMOnIHAMHKn [1]. B JIO6OM cLIyae IOHNMaHNe TEJIOTbI KaK «3HeprHH B COCTOHHN IepExOJa》,T. e. KaK fYHKIIIN N POIeCCA, IOTpe6oBaJIO OTbCKAHNa KooPdHATb 3TOGO IIPOeCCA, T. e. Iapametpa, c Heo6xOINMOCTbIO H3MeHJIOIIeOcR IIpHeRo IIOTeKAHH N OCTaIOIIeOcR HEN3MeHHBM B eRO OTCyTcTBne (B aDna6aTHueckNX cHCTeMax). 3Ty KoOpdHATy P. KJIay3Hyc HAIJI EITem paccMOTpeHHN TORO Ke camoro IINKJIa HIDEaJIbHOIN (o6paTHMOI) TEJIIOBOIM MaIHINbI, OndaKO OH Ha3BaJI eE «3HTpONIIeH」, IIOnUePKHBaY Tem cambIM IIPOTHBIOLOJXHOE TEJIIOPOdy CBoiCTBO 3TOrO 3HEpROHOCHTeJI B03paCTaTB B pe3yJIbTaTe IIoABJIeHHN BHYTpEHHHX HcTOUYHKOB TEJIla. HarJIAJHeE BCErO 3TO IPO8BNIIOCB B 3aIHNC hyaBHeHHN 6aJIaHca 3HTpONHH[11]: $$ \mathrm {d} S = \mathrm {d} _ {\mathrm {e}} S + \mathrm {d} _ {\mathrm {u}} S, \tag {2} $$ rIe coBepHHeHCTBOBaHHaMeTOIOB aHaJIIN3a, = $\delta_{\mathrm{e}}Q^{\mathrm{e}} / T$ n dS = $\delta Q^{\mathrm{e}} / T - \mathrm{NaCTN}$ H3MeHeHHa 3HTpOIIHH, o6ycJIOBJIeHHbIe COOTBeTcTBHeHHo BHeIIHHM TeIIIOOBMeHOM Q" IN BHYtpeHHmHnCToHHKaMH TeIIJa $Q^{\mathrm{d}}$ CorJiaChO 3TOMy BbIPAxKeHHo,JIIO6bIe Heo6paTHMbIe IPOUecCbI, BbIBBaHOT H3MeHeHne OJHO ToTO JIaPAMTePa - 3HTpONnS. T. Sak 3HTpONnI IpeBpaTHJIacB V K03Ja OTNHyIeHNHa 3a «JIIO6yHO N BC8kyo Heo6paTHMOCTb》,XOTa H3NaAJIbHo IIpeDHa3HaJaIacb DJIa OINcAHNr TeIIIOOOMeHa. He H3MeHNlSc cTaTyC 3HTpONn H IOcJIe TOrO, KaK 6hApuyKJInCb BHYTpEHNHe HcTOHNKn HIN CTOKn H y IpyTHx IapAMTePOB, B uAcTHOCTH, y UHCeJI MOJIe k-x BeIeCTB Nk, BO3HKnAOIuNX HIN HCye3AoIuNX B XOJe XHMNUeCKHX peAKIIN.C paIHHPENHEm TepMOINHAMIKn Ha cJIOXHBie (IOJIHBapHaHTNbIe) H HepaBHOBecHbIe (B TOM YHcJIe OTKpbITbIe, 6HOJIOHueCKNe H XHMNUeCKN peaHpyIOUIne) cHCTEmbl, a TaKKe Ha HETeTIIOBbIe H NEIKJNUeCKNe MaIIINHbI, C8Ba3AHbIe c 3HTpONHe IAPAJOIR3MbI cTAJIN BO3HNKaTb IIpaKTNUeCKN B KaJIOJ OblaCTN IIpNJIOJKeHHa TepMOINHAMNKn [20]. 3HTpONn cTAJa «paKOBoi ONYXOJIbIO H «axNJIEcoBOI IaToi» TepMOINHAMKN [21]. OJHaKO IOHNMaHne TOrO, YTO BCE 3TN HeyDaun O6bAcHJOTcII ONbITKaMNIzYuATb Heo6paTHMbIe IPOUeCCbI cpeICTBaMn paBHOBecHOJ TepMOINHAMKN, OCTaBAIOCb IOCTOHNEM JINIIbHEMHORHX yuehix-ODHHOeK [22]. 3THM, IIO-BHINMOMy, H o6barchetc JKNByEcTb 3TOro IOHHTN H OTCYtCTBHe IIOIbITOK IocTpoeHHaTePMoDINHAMKHn Ha 6e3HTpOIIHHOJ OCHOBE. Для ПОСТУЛата 60JIeee aДeKBArHоМеры KOJIHueCTBa xAOtHueCKOrO DnBKeHnI, HgpaIOIIe IIO OTHOIIeHnIO K BHyTpEHHeN OHePrrnUqpoJIb 3HePFOHOCHTJIa, IeJIeCo- oBa3HOo6paTHTbcra K IOHЯTNM«KOJIHueCTBa DnBKeHnI» Mv N<OKBOI CNJIb> Mv2, BBeIeHHbIX eIe B XVII cToJIeTHN P. DeKapTom[23]n Γ. JIeIb6HnIeM[24]. O6e 3TN MePbI OTHOCHINCB K BHYTpEHHEMy KoJIe6aTeJbHOMyDnBKeHnIO. ImEHNO «KHBaIc CHJa» 6blIa IIpeHMeHOBaHaNo IIO ppeIOJIOKeHHIO T. IOHra(1807)B «3HePTrHO», a IocJIe BVeIeHHN IIOTeHHaJIbHOJ 3HePrrn - BO BHyTpEHHIO U. ImEHNO OHa IocJIyXHHa OCHOBoI JII ONPeIeJIeHHN 3HePrrn 3Φnpa U = Mc2Γ. IIIpaMMy(1871); H. H. YMOB y(1873); Jx. TomcoHy(1881); O. XəBncaIpy(1890), A. IlyaHKape(1898)nФ. Xa3eHOpJIIO(1904). 3Ta 3HePrrna BДBoE 6OJIbIIe KINHeTNUeCKO 3HePrrnHaIIpaBIIeHHORO DnBKeHHa NpH TOM Jxe 3NaueHHN cpeIHHeckopocTH v = |v|, KOTOpoe BO3HNKaET B CnCTeMe B pe3YJIbTaTe KOLJIeKTNBHORO (MaKPOsCOJIHueCKOrO) DnBKeHHN Ipn BpaIIeHHN, IIΦΦy3HH N. II.[14]). TOrIa MoJcT Bo3HNKHyTB erO pe3YJIbTHpyIOIIH NMIpyJIbc J = Mv, 3HePrrnaKOTOPORO cTaHOBHTcR BHeIIHRe E_KHH. IIO Mepe Jx 3aTyXaHHa KOIe6aHHN(v→0)N BO3HNKHOBeHHa yCtOHYbIX cTpyKTyp qAcTh b «KNBOI CnJIbI» IepexOHT BO BHYTpEHHHIO IIOTeHHaJIbHyIO 3HePrrno U_HOT. 3Ta 3HePrrna TaKJc cTaHOBHTcR BHeIIHRe E_NOT, ecIIN ΠeHTp MaccbI cHCTeMHI N3MeHJeT CBOE IIOLOKeHHe OTHOChTEJIbHO OKpykaIOIIe cpeJIb.TaKIM O6pa3OM, BHYTpEHHHa 3HePrrna U - OTHIJb He BCEJa ABJIAETcPaCCsEHHo YacTbIO BHeIIHRe 3HePrrn, KaKOBoi ee IpeIcSTaBJIAET 3aKOH coXpaHEHHa 3HePrrn B MEXaHHke HeKOHcePBATNBbIX cHCTeM: $$ \left(\mathrm{E}_{\mathrm{K H N}} + \mathrm{E}_{\mathrm{I N O T}} + \mathrm{U}\right)_{\mathrm{H 3}} = \text{const .} \tag{3} $$ То, что БЫВШЕЕ ПОЯВЛЕНИЕ ЭНТРОПИИ ПРЕДСТАВЛЯЕТСЯ ТАКИМ, ЧТО ОНО НЕ ЗАКАНЧИВАЕТСЯ, И ЕСТЬ ВОЗМОЖНОСТЬ ОБЩЕЙ СВЯЗИ, КОТОРАЯ ПРЕДСТАВЛЯЕТСЯ ТАКИМ, ЧТО ОНА НЕ ЗАКАНЧИВАЕТСЯ. ТАКИМ ОБРАЗОМ, БЫВШЕЕ ПОЯВЛЕНИЕ ЭНТРОПИИ УПРАВЛЯЕТСЯ СВОБОДНО, И ЕСТЬ ВОЗМОЖНОСТЬ ОБЩЕЙ СВЯЗИ, КОТОРАЯ ПРЕДСТАВЛЯЕТСЯ ТАКИМ, ЧТО ОНА НЕ ЗАКАНЧИВАЕТСЯ. ТАКИМ ОБРАЗОМ, БЫВШЕЕ ПОЯВЛЕНИЕ ЭНТРОПИИ УПРАВЛЯЕТСЯ СВОБОДНО, И ЕСТЬ ВОЗМОЖНОСТЬ ОБЩЕЙ СВЯЗИ, КОТОРАЯ ПРЕДСТАВЛЯЕТСЯ ТАКИМ, ЧТО ОНА НЕ ЗАКАНЧИВАЕТСЯ. $$ \left(\mathrm{U}_{\mathrm{q}} + \mathrm{U}_{\mathrm{K H H}} + \mathrm{U}_{\mathrm{I N O T}}\right)_{\mathrm{H 3}} = \text{const.} \tag{4} $$ Takoi IIOxOJ cIIOcO6CTByeT ycTpaHeHHo CO3aBIIeIcIHTyaIHH, KOrJa «COBpeMeHHa JH3Nka He 3HaET, YTO TaKoe OHep Hn» [25.]EcJI N K TOMy JKe IIOI a6coJIHOH TeMNEpaTyPO T(K) IOHNMaTbMEpy HHTeHCNBHOCTH XaOTHueCKORO DNHKeHH, TO BHYTpEHHIO To TEJIIOByO 3HeprHIO UqMOKHO IIpeIcTaBHb IIO aHaJIOrHH co «CBIAHHO 3HeprHei» TJIbMROJIbIa TS B BVNe IIpOH3BeIeHHRAuTQ, IOHNMaI POI OJ KKTcEHCHBHyO MEpy KOJIINcEcbTa 3TOI DNHKeHH[26]: $$ \Theta_{\mathrm{q}} = \mathrm{U}_{\mathrm{q}} / \mathrm{T},\, (\mathrm{\Delta} \mathrm{\mathrm{ж}} \, \mathrm{K}^{-1}) \tag{5} $$ Характеристика ПОДХОДА К ПОНИМАНИЮ ЭНТРОПИИ (Т. е. ХАРАКТЕРИСТИКА, ЯВЛЯЮЩАЯСЯ БЕЗУСЛОВНОЙ). ОТОТ ТЕРМОДИНАМИЧЕСКИЙ ПОНИМАНИЕ ЭНТРОПИИ БЕЗУСЛОВНО ПРЕДСТАВЛЯЕТСЯ ТАКИМ, ЧТО ОНО НЕ ЗАКАНЧИВАЕТСЯ. ТАКИМ ОБРАЗОМ, БЫВШЕЕ ПОЯВЛЕНИЕ ЭНТРОПИИ УПРАВЛЯЕТСЯ СВОБОДНО, И ЕСТЬ ВОЗМОЖНОСТЬ ОБЩЕЙ СВЯЗИ, КОТОРАЯ ПРЕДСТАВЛЯЕТСЯ ТАКИМ, ЧТО ОНА НЕ ЗАКАНЧИВАЕТСЯ. $$ \mathrm{dU}_{\mathrm{q}} = \mathrm{T}\,\mathrm{d}\Theta_{\mathrm{q}} + \Theta_{\mathrm{q}}\,\mathrm{dT} $$ KOPpeKTHO OTPaKaeT N3MeHeHHe BHTpeHHe TEPIOBOI ΘEHPHN KAK BCJIeDCTBHe BHEIIHeTo TEIIIOo6MeHa $\mathrm{Td}\Theta_{\mathrm{q}}$, TaK IINP BO3HNKHOBEHNNBHYTpEHHX HCTOuHHKO B TEIIaΘqdT BCJIeDCTBHe IINCCIIaIIHH. TaKoe IIpeIcTaBJIeHne dUq, cIIpaBeJIINBOCTb KOtOpOro 6yJeT IOITBepKJHeHa HNKe, IIOJIHOCTbU YKJIaIbIBaEtCRA B paMKn IIpaBNI IINΦΦepeHIIHaJIbHO rCHNCJIeHn, YEro He cKaJKeIIb O cJIaRaEMbIX dS h dS b ypaBHeHHN (2).OTJIInue BHTpeHHeI TEIIIOBOI ΘEHPHN UqOT cBIAaHHOJ ΘEHPHN TS, KOTOpYIO TAKE MoKHO INTHepIIpETHpOBaTb KAK ΘEHPHN, CBIAaHHUc TEIIIOBBIM IINJKeHHem, CBIAHO CJIeHOM ΘqdT, KOTOpBI O6paIIaETcB HYNB H3OTepMHueCKHX IPOIIeCCax, HAnpIMep, BXHMueCKHX peAICIHX, rDe $\delta Q = Td\Theta_{q} = TdS.$.B TAkNX cIJyauX IIOHATN CBO6OJHO ΘEHPHN TeJIbMFOJIbIa U-TSh ΘEHPHN ΓI66ca U+pV -TScoxpaHnOT cBoi CMbICJI. OJNaKO B IpyTHX cIJyauX eTO p ZAHnHe IIPoABJIeTCBecbMa HaJIaIHNo, qTO n 6yJeT IOKa3aHO HNKe. ## III. YcTpaHeHne IapaJIIOrH3MOB, Cb3aHHbIX C 3HTpOIIHei Kak 6bIIO IOKa3aHO BbIIIE, IOIMeHa P. KJIay3HycOM IOHATNIA $\langle \text{T} e\text{I}\text{I}\text{I}\text{O}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{I}\text{1}$ KaK KOJIINueCTBeHHoM MepB I ERO BHYTpEHHe TEEIOBOH 3HEpRnU $^{\mathrm{q}}$ 60Jlee y3KHM IIOHNTHEM $\langle \text{T} e\text{I}\text{I}\text{I}\text{O}\text{I}\text{I}\text{I}\text{I}$ IPOecca Q KaK KOJIINueCTBeHHoM Mepo IIOeCCA TEIIIOOOMeHa H BBeJeHne 3HTPOIIIN KAK OOPDINHaTBt 3TOrO IIOeCCA OraPANHJIa TEPMOINHAMHKy paccMOTpeHHem paBHOBecHBIX CnCTEm H o6paTMbIX IPOeCCOB, y KOTOpbIX OTCYCTBYOT BHYTpEHHne HCTOCHNKH TELIIA. 3To IPEBpaTHIO KJIaCCNHecKyUo TEPMOINHAMHKy KJIay3Hyca B TEPMOCTaTHKY, ORpaHNHBAIOHIOUCs H3yueHHem paBHOBecHBIX CHCTEM H 6eCKOHeHc MOJIeHHbIX IIOeCCOB. IocKOJIbKy c IIOBJIeHHem yIOMAHyTBIX BHYTpEHHHX HCTOCHNKOB TeIIIA 3HTPOIIIN MOrJIa TOJIbKO BO3pacTaTB, 6blcJIaH OIIH6OuHbB BBBOID 06 OJHOCTOPOHHe H aIPaBJIeHHOCTH BCEx IPOIIeCCOB BO BCEJIeHHoH N HABRAJIo eH He CBOiCTBEHHUo IIpHpOJe BWeIIe $\ll$ CTpeLy BpeMeHHN. B 3TOM OTHOIIeHHN HECOMHEHHBM IpeHMyIeCTBOM TepMOHMIyJBca $\Theta_{\mathrm{q}}$ IIpePeJ 3HTPOIIHey JBIAETcE rO CIOco6HocTh kAk BO3pacTaTB B IIOueccax IpeXoJa YIOpRAIOueHHbIX φOpM 3HEpRnB V TEJIIOByo, TaK H y6bIBaTbB IPOeCCax 3BOJIIOIHIn, COIIPOBOKDAIOHXXc BO3HNKHOBeHHem $\langle \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I } \mathbb { I }$ «Характеристика»[27]. Имена Таковы процессии Формулирования ВЦ (Макроскопических и Микроскопических) Форм БИЛЕТЦВА ВЕЩЕСТВА. CyIeCTBOBaHHe TepMOHIIyJbCa 6JIaJaET Toi CTeIeHbIO OueBnIDHOCTN, KOtOpA yIOBJeTBOpEET IOHrTHIO ΦeHOMeHOJIoRHeCKO TeOpHN. OH3aBeIOMO cyIeCTByET B CnCTeMAX c MaKcBeJI-60JIbMaHOBckHM paCIppeJeJIeHHem CKOpocTH H HMIIyJbCa YacTHU, YTO OCBo6OJdaEOT OT Heo6XoJIMOCCTN IONcKa IYTei O6OCHOBaHHa CyIeCTBOBaHHH 3HTPOIIHH B HepaBHObECbHX CnCTeMax H eepHMeHHoMCTN K peaJIbHbIM IpoIeCCam. Ero HHTepPiPeTaIHnHe Tpe6yet IIpHBJIeHuEHn MOJIeKUJIrpHOKHHeTHUeCKo H cTaTHcTHKO-MexAHuYeCKo TeOpHN, YTO JeJIaET TepMOdHAMHKU BIOJIHe caMOIOcTaTOUHOI TeOpHn. OctaEtcaIoka3aTb, YTO HCIOJIb3OBaHHe TepMOHIIyJbCa BMeCTo 3HTPOIIHH ycTpaHReT IpaKTNUeCKH BCE YIOMaHyTbIE BBIIIE IapaJIOrH3MbI TepMOdHAMHKn. ### a) Icklouehue hepaeHcme u3 Mamemamuecko2020 annapama mepmoduhamuku I3BecTHO, YTO O6bEINHHeHHoe ypaBHeHne 1-RO H 2-RO 3aKOHOB TepMOINHAMHKN B CJyae Heo6paTHMbIX IpoJIeCCOB IIHNHMaET BNJ HepaBeHCTBa: $$ \mathrm {T d S} > \mathrm {d U} + \mathrm {p d V}. \tag {6} $$ IpiHHHoB O3HNKHOBeHHHepaBeHCTB YBJIeTcTO,TO BOTcyTcTBHe paBHOBecHBA ChcTeMe IIOBJIHOITcBHYTpEHnHe HCTOUYHKN TepIIa,B pe3yJbTaTe KOTopbIXTdS>δQ.AHaJIoTHuHbIe HepaBeHCTBa BO3HNKaIO,T BOo6Ie TOBOPR,Hy npTyHX IpapaMeTPOB Θi,B TOM uHcJIe N IIJI e06bEMa V,KOTOpbI MoKeT yBeJIuHbATbcra IIPIpacIIHpeHHn CHcTeMBI B IyctOTy 6e3 COBepHEHHpa6OTBI $\delta W_{\mathrm{p}}^{\mathrm{H}} =$ pdV. 3TO o6CToRA TeBJcTBO ABJIeTcOCHOBHbIM IIpeIITCTBHeM IJIpiPmHeHHaTePMoIHHaMHueCKOTO MeToJa HCCJIeIOBaHHa K dpYHM INCIIINIIHHaM, H3yuaOHMMpeAIBHbIE (HeCTaTHueckHe) IIpoIeccbl. MeKJy TeM BO3MOKeH HHOI IIOJXOJ K BbIBOJy OCHOBHOro UpaBHeHHa TepMOHaHAMKn, H3HaJaJIbHO opHeHTpOBaHHb Ha HCCJIeIOBaHHe BHyTpEHHe HEPaBHOBecHBIX (HeoIHOPoIHbIX) cHCTeM c IIpoTeKaIOIIHMn B HNX HeCTaTHueCKHMn IIpoIEccamn. 3TOT MeTOn OCHOBaH Ha IIpeDCTaBJeHHN BHyTpEHHe 3HeprHiu UkaKdoii- hCTeHN CBO6Obblc HcTeMbI Hen3MeHHORO o6bema VBapaMeTPOB HEPaBHOBecHOCTcHcTeMbI KaK IIeIoro Zi. 3TN IIapaMeTpb MoKHO HaHTN IIO H3BeCTHOMy pacIIpeJIeHHIO IIIOTHocTH $\rho_{\mathrm{i}} = \mathrm{d}\Theta_{\mathrm{i}} / \mathrm{dV}$ IHx 3HeproHOChTeJIeH e (MacCbI M, YHCla MoJIe k-x BeIeCTB, TepMOHIIyIbcaq, 3apja 3, HMUYIbca J =MV, erO MOMeHTa Lh T.Д.) IO o6bemy cHCTeMbI V. IIprn 3tOM HeoIHOpOIOCTb IHx pacIIpeJIeHHra BBpaJkaETcMaIIeHHem paIHyc-BeKToppa IH zIeHTpa R0 t erONIOJOKeHHB PabBHOBecHom (ODHOpOHOM) COCTOHHRIO, IocJIeHHne OIIpeJIeIOTcH3BeCTHBIM o6pa3OM[28]: $$ \mathrm {R} _ {\mathrm {i}} = \Theta_ {\mathrm {i}} ^ {- 1} \int \rho_ {\mathrm {i}} (\mathrm {r}, \mathrm {t}) \mathrm {r d V}; \mathrm {R} _ {\mathrm {i o}} = \Theta_ {\mathrm {i}} ^ {- 1} \int \rho_ {\mathrm {i o}} (\mathrm {t}) \mathrm {r d V}, \tag {7} $$ Tder - 6eryuaa (3HlepoBa) IpoctpaHCTBHeHHa KoopDHaTa; t - BpeMa. OtcIoJa cJIeIyET cyIeCTBOBaHHe B HeOJHOpOJHbIX CnCTeMaX HeKOTopoRo «MOMeHTa pacIpeJeHnra》, HMeIOIIeTo cMbICJI BeKTopa IIOJIpyH3aIHH CnCTeMBi B caMOM O6IeM IOHNMaHHN 3TOr ToPmHa: $$ Z_{\mathrm{i}} = \Theta_{\mathrm{i}} \left(R_{\mathrm{i}} - R_{\mathrm{i o}}\right) = \int \left[ \rho_{\mathrm{i}} (\mathrm{r}, \mathrm{t}) - \rho_{\mathrm{i o}} (\mathrm{t}) \right] \mathrm{r d V} \tag{8} $$ c IIeYOM $\mathbf{R}_{\mathrm{i}} = \mathbf{R}_{\mathrm{i}} - \mathbf{R}_{\mathrm{i0}},$ Ha3BaHbIM HAMN «BeKTopom CMeIIeHHA». IIOCKOJIbky B paBHOBeCnH $\mathrm{R_{io} = 0}$ $\mathrm{dZ_i =}$ $\Theta_{\mathrm{i}}\mathrm{dR}_{\mathrm{i}}$ TOBHyTpEHHRA 3HePnHcNCTeMbI B IeJOM U KaK cyMMa IIapIIHaJIbHbIXHePnH $\mathrm{U_i = U_i(Z_i)}$ cTaHOBHTcA yHKIIHe H3aBHcHbMbIX IIepMeHHbIX $\Theta_{\mathrm{i}}$ IN $\mathbf{R}_i\mathbf{:}\mathbf{U} = \Sigma_i\mathbf{U}_i(\mathbf{Z}_i)$.B TaKOM cIyuae eIIOJIbI dHΦepeHnHaJI MoKHo IpeIcTaBHTb B BNIE ToKJDECtBA [27]: $$ \mathrm {d} \mathrm {U} \equiv \Sigma_ {\mathrm {i}} \Psi_ {\mathrm {i}} \mathrm {d} \Theta_ {\mathrm {i}} + \Sigma_ {\mathrm {i}} F _ {\mathrm {i}} \cdot \mathrm {d} R _ {\mathrm {i}}, \tag {9} $$ IgHe $\Psi_{\mathrm{i}}\equiv (\partial \mathrm{U}_{\mathrm{i}} / \partial \Theta_{\mathrm{i}})_{\mathrm{R}}-$ yceHneHHbIe 3NaueHnO o6oIIeHHbIX IOKaJIbHbIX IIOTeHIIHaJIOB $\psi_{i}$ (a6coJIHOtHOJ TeMIIpeaTypblTH JaBJIeHHe p, XHMNEcKOro IIOTeHIIHaJIak-RO KOMIOHeHTa $\mu_{k}$ erO 3JIeKTPuYeCKOro $\varphi$ n rpaBHTaIINHOHOrO IIOTeHIIHaJa $\psi_{g}$ H t.II.); $F_{\mathrm{i}}\equiv (\partial U_{\mathrm{i}} / \partial R_{\mathrm{i}})_{\Theta} = \nabla U_{\mathrm{i}} -$ cnJIb B hX o6IeΦH3NueckOM IOHNMaHHN. JIeHbI 1- cyMMbI eTOrO ToKJdecTBA OINcBIAOT IIpoueccbI IpiHO6peTeHHN HIn yTpaTbI IapIIaJIbHOH eHepHH Ui He3aBnCHMO OT TOrO, Yem OH N BbI3BaHbI: IpeHocOM eHeproHOchTeJIg $\Theta_{\mathrm{i}}$ Ype3 rpaHnBc CHcTeMbI HIN IOBJIeHHem eTo BHyTpEHHHX hCToUHHKOB. JIeHbI Je2- cyMMbI OINcBIAOT BHyTpEHHIO pa6OtY, COBepuaemyIO pIn IpeBpaIeHHN B i-Io eHepHHo Ui npyTHx eOpM, T. e. eBHyTpEHHHne hCToUHHKn. B OINHpOJIbIX cHCTeMax (dR=0) 3TO BBipaeHHe IepExoIHIT B o6beHNHEHHoe ypaBHeHne 1-TO n 2-TO Haayl KJIaccuYeckoI TepMOINHAMKN IIOLINBaHPaHTbIX cHCTe dU $\equiv \Sigma_{\mathrm{i}}\Psi_{\mathrm{i}}d\Theta_{\mathrm{i}}[9]$ ТЖИАБХОЕ ИОКТОНХЧТОБ ТОКЖЕДЦТБА(9)КОКТОХТ Б ТОМ, ЫТО ЫХО ЫЦТПАРЭТ НЕОИПЕЖЕИЛЕХНОЧТБИ ИООХТН ИЯПИЯЖИБХО 3ХЕПРИН ЙИО60И ЦТЕИЕХН ЦБО6ОДБИ ХЕПАБХОБЕЧНОЙ ЧКЦТЕМБИ УИН ЯЭТ ЕИНХОЕИЛЕХНЕ ИООХТН ЦЖИБИ ФИКАК ЕИГАИДХЕТА. ЙЕЦТБХТЕЖИБХО, БИПАЯКЕХНЕ ФИ$\cdot$ДРЖИЕКО ЙИПЕО6ПА3ОБАТБ К БНДУ ΘДΨ КАК АХАИИОЙ ПА6ОТБИ РА3А Б ИОТОКЕ ВДП, ИНИН К БИПАЯЕХНИО Х;ДТТ, ЕЦИН ББЕЧТ НИОХТН ТЕПМОИНАМУЕЧНОЙ ЦЖИБИХ =ФИ/ΘИ ИОТОКА Й= ДЗ/ДТ= ΘВИ, КАОББИМН ОИЭПНПЫЕТ ТИИ. В ТАКОМ ЧИЮАЕ БИПАЯКЕХНЕ(5)ИН(6)ЦТАНОБРАТЦЯЧТБИМ ЦИЖЮАЕМ О6ИЕРО БИПАЯЕХНИО ЙАПИЯЖИБХОЙ 3ХЕПРИН У=Ψ;ΘИ ЙИО60И ЦТЕИЕХН ЦБО6ОДБИ ЧКЦТЕМБИ КАК ИПОИХБЕЕНЕ ЭКОЖЮЕЦБЕЧНОЙ И КЯЕЦБЕЧНОЙ МЕПБЛ, А ТЕПМОИНАМУЕЧНОЙ ЦЖИБИХ ЫН ИОТОКН ЙПХНО6ПЕТАТ ОЖХО3НАУХИМ ЧМБИЦЖИ ХАИПРЯКЕХНОЧТБИ 3ХЕПРИМОХОЧТЕЖИХ ЕРО ХМИИБЦА Bn30JIHPOBaHHbIX CnCTeMaXn3MeHeHne IpaMaTePPOB $\Theta_{\mathrm{i}}$ o6yCIOBJIeHO NCKJIOHTeJIbHO BO3HNKHOBeHHem Hx BHyTpeHHNX HcTOUHHKO bO/dt, TaK YTO3aKOH COxpaHeHHN 3HeprHH B Hnx dU/dt=0 IIpHHMaet IpoCToB BVd: $$ \Sigma_ {i} \Psi_ {i} d \Theta_ {i} / d t + \Sigma_ {i} X _ {i} \cdot J _ {i} = 0. \tag {10} $$ ЯНКАЖИБХОЧТБ 3ТОРО 3АКОХА КОКТОХ Б ТОМ, ЫТО ЫТБЭПКЯЕТ ХАЖИНЧНЕ ХЦТОУХХКОБ ХЖИН ЦТОКОБ 3ХЕПРОХОЧТЕЖИ ДО/ДТ И ТОЖИБКО Ы 3ХТПОИИХ, ХО Б 06ИЕМ ЦЖЯЕ ЙИО6ОБ ЦТЕИИХН ЦБО6ОЖБЦ ЧКЦТЕМБИ. 3ТО О3ХАЯАТЕ НЕ ТОЖИБКО БО3МОХОЧТБ БО3ХНИКХОБЕНХ Х3ОЖИХПОБАХХОХ ХЕПАБХОБЕЧНО ЧКЦТЕМЕ ХЕ ХОББИХ ЦБОИЦТБ И НЦЯ3ХОБЕНХ ЦТАПБИХ, Т.Е. Е 3БОЖИОИИХ ИН ХХБОЖИОИИХ, И ОТЦЫТЦТБХЕ Б НЕ 3АКОХОБ КОХПАХЕЙ ИИО6ОТО Х3 3ХЕПРОХОЧТЕЖИЕН[29], ЫРО КОБПЕМЕХА Ж3ХКА НЕ ИОНЯКЦЕТ Ц НПИРО ЧТОПОХБИ, БИПАКХЕНЕ(10)ДАЕТ БО3МОХОЧТБ ХЦЦЖИЕИОБАХНХ ХЯТПЕХХНХ ИИПОИЕЦОБ Б Х3ОЖИХПОБАХХИХ ЧКЦТЕМБИХ, НЕ ПАЧЛЕХН ХН ХА 3ЖИЕМХТАПХИЕ О6БЕМБЛ ДВН ХЕ ЫБЕЖУНБА ТЭМ ЦАМБИМ ЯНЦИО ЦТЕИИХН ИХ ЦБО6ОББИ ДО 6ЕККОХЕОЧТ. ПИН О'ТОМ КОХПАХОТЦ ТАК ХА3БИАЕМБИЕ 'ЧКЦТЕМХБИЕ' ЦБОИЦТБА 06БЕКТА ХЦЦЖИЕИОБАХНХ, ОТЦЫТЦТБХЕ Б ЕРО ОТЖИБХИХ ЧАКТХ HaKoHei, ypaBHeHn (9) n (10) Jaet eHnHoe OIIpeJIeIeHne IIOHrTHN, KOToPbIMN OIIepnpyET TepMOHHaMHKa, MExaHHKa, 3JIeKTpoDINHaMHKa HIpYrHe IINcIIINIIHNbI. 3TO OTKpbIBaET BO3MOxHocTb Hx IaJIbHeIIIErO cHHTe3a [30]. ### b) YcmpaHene HneOpedeJehHocmu nomeHuaJa KOMNoHeHma HaJaIO IprHMeHeHHO paBHOBechOH TePMoHNHAMNK K HCCJIeIOBaAHNIO IpoIeCCOB IINΦΦy3HH, XHMnueCKHX H a30BbIX IpeBpaIeHNI, CB8aHHbIX c H3MeHeHem MaccBi H COCTaBA HCCJIeIyEOM CnCTEmBI, IIOJOKHJIN pa60tBI JK. Tn66ca[31]. OH IpeoIoiJIeI ORpaHHueHHocTb KJIaccNueckOi TepMOHNAMHK ROMOTeHHbIMN CHCTeMaMH OCTPOUHMHeIIHMM CIIOCo6OM, IpeIcTAbVB 3aKpbItyO B IeIOM CnCTeMy KaK COBOKYIIHOCTb OTKpbITbX OINHOPOIHbIX IIOChCTeM, T. e. CBEJYBHTpeHHNE IpoIeCCs H3MeHeHNN CoCTaBA CnCTeMBI B XHMnueckHX peAKHJX, IpoIeCCax IInbIbIy3HH N T II. K IIOpIeCCam AHeIIHeRo H3bHpTaJIbHOr MAccOO6MeHa Yepe3 IIOJIpOHHaEMbIE Mem6paHbI, BOo6paKaembIE BEHTJIH N T. II. OJHaKO HeKOTOpBle IpoIeCCs B OTKpbITbX CnCTeMax OKa3aJIncb HaCToJIbKO CBOeO6pa3HBIMN, YTO «O6bYCHNTB H IOITBepIHTb IH 3aKOHomePHocTH Na OCHOBE KJIaccNueckHX KOHIeIIH N He IpeIcTaBJareTc BO3MOxHbIM» [32]. B YacTHoCTN, HapdY C TEIIIOo6MeHom N pa6otoi pacIIIHpENHv B TaKHX CnCTeMax IIOBHNICb eIe IBa BVIda 3HEPFOOOMeHa: O6bHyBIM Maccoo6MeH (IepHoc BeIeCTBa 6e3 H3MeHeHNa COCTaBA CnCTeMBI) N H3bHpTaJIbHBI Maccoo6MeH (INΦΦy3Nk k-X BeIIeCTB Upe3 rpaHHbI CHTeMbI, CB8aHHaN C H3MeHeHHem COCTaBA CnCTeMBI 6e3 H3MeHeHNA ee MacCbI). В ТАКОМ ЧИЮАЕ ХЯТПЕХХН 3ХЕПРГН ЧКЦТЕМБЛ У ЦТАНОБХТЦ ЯХНИЕ ЯЧЕЖИ МОЖИ Н КБЦЕХ К-Х Е3АБХЦМБИХ КОМИОХЕТОБ Х А3 ЦКЦТЕМБЛ У = У (S, V,$N_{k}$), А О6БЕИИНХХЕОЕ УПАХЕХНЕ 1-РО Н 2-РО НАЖ ПАБХОБЕЧОХ ТЕПМОХНАМХК ИИПХМАЕТ БНД КООТОХИЕН ИХ66ЦА[9]: $$ \mathrm {d} U = \mathrm {T d S} - \mathrm {p d V} + \Sigma_ {\mathrm {k}} \mu_ {\mathrm {k}} \mathrm {d N} _ {\mathrm {k}} \tag {11} $$ Ри С, В - ХЯТПЕХХЯ ыхепхра, ыхтпоЖИХН И О6БЭ ОТКПБИТОХ ЧКЦТЕМБЛ;P = -(∂U/∂V)T,Nk,T = (∂U/∂S)V,Nk А6КОЖИОТХБИЕ НАБЖИЕНЕ И ТЕМИИПАТПЯУК К= (∂U/∂Nk)S,V,Nm - ХМНУЕЧНОЙ ИОТЕХНАЖИ КОМИОХЕТОБ, НАДЖДЕХНИ Б ЯЦИОБХХ ИОЦТОАХЦТБ С, В Н УХЦЯ МОЖИЕН 3aHcBbA 30 To BbipaKeHne, H66c IJIaRaJI, YTO $\langle \text{三} \rangle$ HeprnU, OueBnIHO, 6yJeT cyHKIIeN S, VIMK» KaK He3aBHCMBbIX IIepMeHHbIX, a IepBbI N BToPOr qJIeHbI (11) IIo-IPeKHeMy xapaKTePn3yIOT TeJIIOO6MeH n pa6Ory pacIIIpeHHa paBHOBecHOI cHCTeMbI. OJHaKO B JaJIbHeIIeM [20] bBIAChNIIOcB, YTO 3TO DaJIeKO He TaK. 3HTpOIIIN S = sMn o6bE M V => M MHOROKOMIIoHEHTHOI cHCTeMbI C Heo6XoJIMMOCTbIO H3MeHReTcR Kac IIpn MaccOO6MeHe (M#const),TaK H IIpn H3MeHEnH eCocTaBaNk/N):S = sKn, V = uKn IIpn HEn3MeHHbIX IIapIIaJIbHbIX MOJIaRbIX 3HTpOIIHX SkyH 06bEMaxo k KomIOHeHTOB. 3TO ABHbIM o6pa3OM HApYIIaOT ycIOBHe IIocToAHCTBa 3HTpOIIIN SN 06bEme V B ypaBHeHH (11), 3aIOJKeHHoe DJK. Tn66com IIpn OIIpeJIeHHn IIOHJTHn XHMNUeCKOTO IOTeHIJaIa μk, BCJIeCTBHe YeRo 3HaueHne IOTeHIJaIa KOMIOHeHTa B IIpoIEccax MaccOO6MeHa, IIHΦΦy3HH N OCmoca OKa3bIBaOTcRA pa3JIuHbIMn CO BcEMN BbITeKaIOIHMM dJIa TepMOXHMn IOCJIeCTBHMn [20]. ИОИОЖКЕХНЕ МЭРЭТЦР,ЭЦЖИН БМЭЦТО 3ХТПОИИХ КАК КООПИНХАТБИ ТЕЖИИОО6МЕХ ХЦИОЖИБ3ЫЕТЦРА ТЕПМОХМНУБЦ ОККАК 6ОЖИЕ О6ИИ ИИПААМЕТП, Х3МЭХАНИОИИХЦР НЕ ТОЖИБКО ИПР ТЕЖИИОО6МЕХЕ, ХО Х Б ИПУЕЦЦА ДНФИЮ3HH Н ОЦМОЦА. В 3ТОМ ЧИЮАЕ ИОЦТОАХЦТБ ОГ РАПАХТНПЫЕТ ХХ ОТЦЫТЦТБХЕ, ТАК ЫТО ИПОХ3БОИДХА МУК = ДУК/ДНК ОЖХО3НАХХО 3АЯЕТ ЫЖИБХУО БЭЖУННХ 3ХЕПРНК-РО КОМИОХЕТОБ, ББОИМИМО Б ЦКЦТЕМЫ. 3ТО КООТБЕТЦБЫЕТ 3АИНЦЦКООТХОИИЕРА 66ЦА(11)Б КОМИОКАТНОЖ ФОПМЕ, ОЧОБАХНО ХА ТНИОТЕ3Е ЙИОКАЖИБХОРПОБАХОБЕЧР[14]: $$ \mathrm {d} \mathrm {U} = \Sigma_ {i} \psi_ {i} \mathrm {d} \Theta_ {i}. \tag {12} $$ ИПН 3ТОМ ЦБО6ОХБИЕ 3ХЕПРХН ТЕЖИБМРОЖИУА Ф И И#66ЦА Г КОХПАХРАХОТ ЦБОИ ЧМБЛН Х БЭЖУЧХХ, ИОККОЖИБКИ Б 3ТОМ ЧИЮАЕ ДУ = ТДТС ### c) UcmpaHene npou3e0a 8 b6ope dBuKyuux cun pealbHbIX npouecco8 Korla RoboprO opeBOJIOHIN B hNKe XX CToJIeTHRA, TO O6bIuHO HMeOT B BVNu KBAHTOBUo MExaHNKY (KM) n TeOpHIO OTHOCHTeJIbHOcTH (CTO n OTO). MekJy TeM HAp Iy c HMMN B Iep Np Tp 0n TOrO Je cToJIeTHRA BO3HHKJa eIIe OHa He MeHee fHyIaMeHTaJIbHaNr TeOpHra - TePMoDInHAMHKa Heo6paTMbIX IIpoIeCCOB (THII). 0Ta TeOpHra, IIOJIyUHBIIa Ha3BaHHe TepMOINHAMKNH Heo6paTMbIX IIpoIeCCOB[12-14], 6a3npoBaJIacb Ha IIOHOpeCKHX pa6OtaXbUdIeero HO6JIeBCKORO Jlaypeata J. OH3aRepa[33], KOTOpbI B1931r. IIpeJIOxHI «KBA3HTepMOINHAMUeCKYIO» TeOpHIO CKOPocTH HEO6paTMbIX φH3NKo-XHMUeCKHX IIpoIeCCOB. 0Ta TeOpHra BIIepBbIE IIpeOJOJIaOgPaHnueHHOCtB TepMOINHAMKN KBA3HCtATNHueCKHMn IIpoIeCCAMn[11-14]. OChOBHbIMN BeJINHHAMn, KOtOpbIMN OIIepHpyeT OHa, YBJIaOTcckAJIpaRbIe «TepMOINHAMUeCKHe» CNJIb Xi H «IIOTOKH» Ji. 0TH BeJINHHbI HAXOJATC B Hei Ha OCHOBE BbipaeHnIckopocTH BO3HNKHOBeHHN 3HTPOIIIN dS/dt KaK $\phi$ yHKIIHn HeKHX IapaMeTpOB $\alpha_{i}$,XapaKTepH3yIOIIHX ydaJIeHHe TaKHX cHCTeM OT paBHObecH: $$ \mathrm{dS}/\mathrm{d t} = \Sigma_{\mathrm{i}} \left(\partial \mathrm{S} / \partial \alpha_{\mathrm{i}}\right) \mathrm{d} \alpha_{\mathrm{i}} / \mathrm{d t} = \Sigma_{\mathrm{i}} \mathrm{X}_{\mathrm{i}} \mathrm{J}_{\mathrm{i}}. \tag{13} $$ OДнako IapaMeTpbl αi paBHOBeCHoi TepMOIHAMHKe 6bIIN 3aBeIOMo HeH3BecTHbI.IIO3TOMy eTo TeOpHg ocTaBaJIacb, IIO cyIeCTBy, IycTBIM φopMaJIH3MOM IO Tex Iop, Ioka IpyTOB 6byUIIH Ho6JIeBCKn JlaypeAT H. IIpHroKHH He IpeIIOKJI MeTOHaxOXJDeHNH 3THX BEJIuHH IJIY «CTaIIHOHAPbIX» HeO6paTHMbIX IpoIeCCOB [9]. IJIa 3TOrO OH BbIDHNUJI rHIOTe3Y IOKAJIBHOpaBHOBeCnH, COJIaCHO KOTopoB IN B 3JIeMeHTax O6BJEMA KOHTINHyMa dV cyIeCTByET paBHOBeCne (HeCMOTpr Ha IIPOTekaHHe B HNX HeCTaTHueCKHX IPOeCCOB), TaK YTO HX COCTOHNHe XapaKTePH3yeTcTc TEM JxHa6Opom IpeMeHHbIX $\Theta_{\mathrm{i}}$, YTO H B paBHOBeCnH (HeCMOTpr Ha IIOBJIeHne IIOIOJIHNTEJIbHbIX TepMOIHAMHueCKHX cJI Xi), a K HNM IIPHMHMBI BCE COOTHOIIEHNN paBHOBeCHoi TepMOIHAMHK (HeCMOTpr Ha HeH36eKHBI IIepExoI INX B HepaBeHcTBA). IIpnBceCBOe BHyTpeHHeI IpoTHBOpEHNBOcTH 3Ta TnIOTe3a IIo3BOJIA HaxOJNTb BEKTopHbIe CJIbI Xi I IOTOKN J, HCIOJIb3yJ3aKOHbI COxpaHeHHa Maccbl, HMIIyJIbca, 3apJaI H3eprHIN, B3aTbIe H3 IpyTHX DHCIIINIH. 3TO Tpe6OBaJIO COCTaBJIeHHa IOBOJIbHO CIOJKBIX H rPOMO3IKHX ypaBHeHH Nx 6aJIaHCA c CEJIbIO BbIeJIeHHN H3 dS/dtTo Hx YacTH nDuS/dt, KOtopaY XapaKTepH3yeT «IPoH3BOJcTBO» 3HTPOIIHH BCJIeCTBHe IINCCIIaIIH. OHaKO H B 3TOM CJIyae pa3IOJKHTb «IPoH3BOJcTBO 3HTPOIIHH> Ha COMHOJKeJIH Xi J MoKHO MHOJCeTBOM CIOco6OB. 3TO O6ycJIOBNIIO H3BeCTHbI IIpOHIBOJ B HX φH3HueCKOM CMbICJe H pa3MepHoCTH. TaKoi IIpOHIBOJ COBepHEHH HeOIOUcTHM, KOrJa peYb NIdet He o paccseHHN 3HeprHn, a O IIpoIeCCax eE IIpeo6pa3OBAHH, IIOCKOIbKy HcKaJaET HxaP3MePHocTb HΦH3NUeCKN CMbICJ COMHOJKeJIe [36]. 3TO T HeIOCTaTOK ycTpaHAreTc, ecJIH CNJIbXiN IOTOKN J, HaxOJNTb HeIOspEcdTbeHHO N3 COOTHOIIeHH (10). IIpn 3TOM OTIIaJAE THeo6XoIMCoCTB B COCTaBJIeHHN yPiomAHyTbIX ypaBHeHH 6aJIaHCa, YTO COCTaBJIEr OCHOBHyO TpyDnocTb IIpHIOKeHH NTHI K pa3JIuHbIM cnCTeMaM [14]. ### d) YcmpaHeneHue «PpuOpumema» menloBozo paBnoBecua B yke yIIOMAHyToI pa6Ote [31] Jx. H66c, IIpHMeHЯ B KaueCTBe ycIOBnpaBHOBecn MHHMym BHyIpeHHei 3HeprHn U,HaIIeJI ycIOBn TaepMHueCKOro, MExaHHueCKOrO I MaTePHaJIbHOpaBHOBecn rTepeoreHHbIX cHcTeM: $\mathrm{T}^{\prime} = \mathrm{T}^{\prime \prime}$ (TeIIIOBOe paBHOBeche); $$ \mathrm{p} ^ {\prime} = \mathrm{p} ^ {\prime \prime}; (\text{MexahnueckoepaBHOBeche}) \tag{14} $$ $$ \mu_ {\mathrm{k}} ^ {\prime} = \mu_ {\mathrm{k}} ^ {\prime \prime}. (\text{MaTepHaJbHoepaBHOBeche}), $$ TIDE OHIMN IIBYMIIITpHXaMH O6O3HaYeHb TEIMIepaTy a T,IaJIeHne p H XHMnueckn IOTeHuaJk-Kro BeIIECTBa MHOROKOMIOHEHTHOI CHCTeMBI. HNoI pe3yJIbTaT IIOJUyAeTcR IIpH HcIIIOJIb3OBAHHN B KaueCTBe KpHTepn paBHOBeCnR IIpHHIIIIa MaKcIMMy 3HTpOIIHN S = S (U, V, Nk) = max, BapHaIINr KOtOpoi δS IIo 3HePInn U, o6bEmy V nHcJIaM MoJIe Nk IIpHBOJNT K ycIOBnM paBHOBeCnR[13]: $$ T ^ {\prime} = T ^ {\prime \prime}; p ^ {\prime} / T ^ {\prime} = p ^ {\prime \prime} / T ^ {\prime \prime}; \mu_ {k} ^ {\prime} / T ^ {\prime} = \mu_ {k} ^ {\prime \prime} / T ^ {\prime \prime}. \tag {15} $$ HecIOJHO 3aMeHTb, YTO JBa IOcJIeHNX paBeHCTBa Tpe6yOT IIpeIbapHTeJIbHOrO BbIIIOJIHeHHY cIOBnA TeIIIOBOrO paBHOBecnT$\mathbf{T} = \mathbf{T}$. OTcIOJa o6bIuHO JeJIaETcB bIBoI O6 o6obO prOI HTeIIIOBOrO paBHOBecn, 6e3 KOTOpO rKO6bI He MoKet HaCTUINTB Hm MExAHueckoe, HN MaTePnaJIbHoe paBHOBecne. HecooTBeTcTBne 3TOrO pe3yJIbTaTa 3KcIepHMeHTam, Iprn KOTopbIX Ha6JIIOdaJIocb IIpeKpaIeHHem 6MeHa k-MH BeIeCTBaMn B YcIOBHX HApUIIeHHa TEIIIOBOrO paBHOBecnH, 06IeH3BeCtHO[13]. MeKJy TeMcTppeMJIeHHe THII yIOBJeTBOPHTb ycIOBnAM(13)IIpHBODHT K TOMy, YTO TepMOIDHAMHueckne CJIbI$X_{\mathrm{i}} = \Delta \psi_{\mathrm{i}} / \mathrm{T}_{\mathrm{B}}$THII B 063aTEJBHom IopRdKe coDEpKAT TemIEpaTyPy, YTO DeJIaET pa3HOpOIHbIe CJIbI B3aHMOCBraHHBMn. IocJIeDHee I IOcIJyKJHIO ocHOBo JI. OH3aRepy DIA IOcTUYINPOBaHHN 3ABHCIMCTCNCKOPCTNIIO6Oro PeJAkaIHNOHHORIO IpOIEcca J ot BCEx IeJCTByUoiHx B cnCTeme cJI Xi, OIIIN6OuHOCtB KOtOPo Ro 6yIet IOKa3aHa HnKe. TaKM O6pa3OM, 3aMeHa 3HEpRETHuecknx KpHTepHeB paBHOBecn 3HTPOIIINHBIMn HE IipocTo NCKaJkaET YcIOBnMAxAHueCKoro IN MaTePnaJIbHO rPaBHOBecnH, HaJIeEHbIe FIn6com, Ho IN MeHJeT pe3yJIbTaTbI TepMOIDHAMHueCKoro aHaJIIN3a. ### e) YcmpaHeHue KOHfLukma THN c noHaMuem pe3yIbmuPyoue cuIbI THII o6oRaTHJIa 4H3Hueckyu MbICJb XX cToJIeTHn pIOM IIINIOB 6IeΦH3HuecKOrO 3apaKTepa H yCTaHOBHJIa IIINIHINHaJIbHyIO BO3MOxHOCtB caMOOPraH3aIHH B CnCTeMax, DaJIeKHX O paBHOBecH. OHaBePhyJIa B TepMoINHaMHKy IOnHrThe cHJIb, YtpaYeHHoe co BpeMehC. KapHO, H O6BJcHNJa MHOxKeTBO 0f0eKTOB, BO3HNKaIOIiX IIpN OJHOBpeMeHHOM IpoTEKaHH B OJHH N Tex Jke O6JIacTAX IIPOcTpaHcTBA HeCKOJIbKHX pa3HOpOJbIX Heo6paTHMbIX IIpoIeCCOB. BKJIaI THII B IIap aINrMy XX cToJIeTHN 6bJI OSeHHe IIpcSyKdEHHem IByx Ho6eJIeBckHX IIpeMn(JI. OH3aReP, 1968, IV. IIpHroKHH, 1977). OДнako THП Do cHx Iop 6a3npyeTcH Ha IIpHnIiIe BO3paCTaHH NHTPOIIHH H pIe TnIOte3 H IOCTyJIaTOB, YTO JINIIaET eE Heo6XoJHMoN POJIHObI H CTpoROCTH. OdIH N3 TaKHX IOCTyJIaTOB - IIpHnIiI HInHeHocTH JI. OH3aRepa, corJIaChOHTo KOTOpOMy JIo6oH He3aBHCHMBy IOTOK J(TeIIJa, BeIeCtBA, 3apJa, HmIIyJbCa n T. I.)JInHeHNo 3aBNCNT OT BcEx JeIcSTByIOIIHX B cHcTeMe TepMOINHAMHueckHX cJI Xj[33]: $$ J_{i} = \Sigma_{j} L_{ij} X_{j}, (i, j = 1, 2, \dots n) $$ TIDE $\mathrm{L}_{\mathrm{ij}}$ KO3ΦΦHIIHEHTb IIPOIOPIOHOHaJIbHOCTH, HA3BaHHbIE OH3aRepOM «ΦeHOMeHOJIOrHuec-KHMH», KAK N cAMN 3TN ypaBHeHH. TJIaBHbI CMBiJI 3THX 3aKOHOB 3aKJIHOaJIcB B yTBepKJdeHnN BCEo6IeB 3aHMOCB3aHHOCTH peaJIbHbIX (HeCTaTHuecKHX) IIpoIeCCOB. IIOJIOKeTIbHbI 3NaK Bcex YJIeHOB cyMMbI(16)JaJI OCHOBaHne HJee «CnHEpREtH3Ma», T. e. ycJIeHnE$\phi \phi$ekTA B pe3yJIbTaTe KOOIIpeaTHBHOrO JIeCTBnI. OJHaKO 3TH UpaBHeHn paCXoIHINCb C 3aKOHAM TeIIIOIPOBOJHOCTH (Фурbe), IINΦΦy3HN (Фнka), 3JIeKTPoIIPOBOJHOCTH (OMa), ΦIIbTPaIIIN (ДapcH), BЯЗКОТ rpeHnR (HbIoToHa) n T. II., B KOtOpBX yIOMaHytbie ITOKIn HMeJIH eINHCTBeHHyIO(pe3yJIbTHpyIOIyIO)DBHKUIIyO cnIy F, BBIPAkaIOIyOocr IpaIHeNTbITeMIIepaTybl, XHMNHecKOrO H 3JIeKTPuYeCKORO IOTeHuaJa, JaBJIeHnR, cKOpOCTn H T. II. $$ \mathrm {J} _ {\mathrm {i}} = - \mathrm {L} _ {\mathrm {i}} \mathrm {F} _ {\mathrm {i}}, \tag {17} $$ Ko3ΦHHeHTbI Li B 3THX 3aKOHaX JBJIJIHcB ΦyHKIIJHM IIapaMeTPOB H cTpyKtypbI cHCTeMbI H He 6blIN BeJIYHHAMN IOCTOAHHBIMn, TaK YTO 3aKOHbI (14) 6blIN HeJIHHeHbIMn. IIO3OM OTHeceHne ypaBHeHn (16) K «ΦeHOMEHOJIOHueCKHM» (IOJIyUeHHbIM H3 OIIbITA) He COOTBeTCTBOBaJIIO, cTporo TROBOPr, JeIcTBHTeJIbHOCTH. 3TO OTHOCHTcR H IOJIOKeTIbHOMy 3HaKY BCex YJIeHOB MaTPnuHoi φOpMbI (15), YTO, KaI IOKa3aJI X. Ka3HMnp [12-14], cIIpaBeJIINBO IaJIeKO He IJIbCEx CJI. Kpome ToRo, OCTaBAIOscb COBepIIeHHO He IIOHHTbIM, KaKIM o6pa3OM MOrTy 6blTb CB3aHbI 3aBeJOMO He3aBHCMBie IOTOKN. IIpHnHy yka3aHHOro HecooTBeTcTBnRA MOxHO IIOHBy, ecJIN HCXODHTb He H3 NIDEN «HaIOKeHHN» (cymmnpOBaHH) HCTOuHHKOB 3HTPOIIHH, Bbl3BaHHbIX DeIcTBHe mpa3HOpOJIbIX IHCCHIIaTHBbIX cJI Xj, a H3 MEXaHNKn, YTBepKJaIOUeI cyIeCTBOBaHne pe3yJIbTIpyOUIe F;OTHX cJI. B H3OJIHPOBAHHbIX cHCTeMax cyMMa BHYrpeHHX cJI $\Sigma_{i}F_{i}(i = 1$ $2\dots n)$ BCERda paBHa hyJIO. 3To O3Haayet, YTO BcGJIacHH C Tp eTbHM 3aKOHOM HbIoTO Ha JIO6yIO III IIpHIOJKeHHbIX cJIHNX F MoKHO BBIPA3HTb cyMMo n-1 cJI peAKIIHN Fj HHO, j-ro poJa: F= - $\Sigma_{\mathrm{n}-1}\mathrm{F}_{\mathrm{j}}$ IocKobky $\mathbf{X_i} = \mathbf{F_i} / \Theta_i$, 3aKOBHI (16) MOxHO IIpeIcTaBHb IMatprHNo fOpMe, IIOo6HoN (15): $$ J_{i} = L_{i} \Sigma_{\mathrm{n}-1} (\Theta_{j} / \Theta_{i}) \, X_{j} = \Sigma_{j} L_{i j} X_{j}. $$ Ko3ΦHHeHTb Lij =LrΘj/ΘiB 3TOM BbipaKeHHN O6beHHJOT B c6e KHNHeTHUeCKHe H TepMOINHAMUeCKHe φakTopbI, YTO H O6bAcHJeT, IOncEmy Hx aHaJIOrn Lij B (14) He HMeIOT CmblcJa HN Tex, HN dpyTHx [12]. TaKHM o6pa30M, IIOBJIaeTcB O3MOXHOCTb O6OCHOBaTB MaTpNHyO fOpMy 3aKOHOB IIpeHoCA, He IIpH6eRa K HX IOCTUYINPOBAHNO, H B TO Jx BePem yIIpocTHTb HX IIyTeM HaxOxJDeHHN pe3yJIbTHpyUOIIe DBNKUIIe CNJIb JIO6OTo He3aBNCMHOrO IpoIecca H IIpNBcEHHN 3aKOHOB (16) K HX «DInaRohAJIbHoH» fOpMe (18) [35]. ### f) YcmpaHHeHue «DucKpUmHaHuu» menIObIx MaunuH IprHrTO cHTaTb KaK HeUTo caMo co6oB pa3yMeIOIIeecra, YTO MaKcHMaJIbHbI KIIJ IHO6oH HeTeJIIOBOH MaIIHHbI(MExaHNueckO, rHIpBaJIINueckO, 9JIeKtpNueckOHI. T.I)6JI30K K eINHHIE, TO Ia KaK JJIa TeJIIOBBIX MaIIHH-IBHrAteJIeH, 3HePrH K KOtOpbIM ПОДВОДТСЕВФОмTeПЛaQ1,OHOrpaHnueH TeMIIepaTypamNПОДВОДАИOTBOДaTeПЛaHaПraKTHKe peIko IIpeBbIIaer$40\%$ TaKaJa 《INCKPmHnHaIINa》 TeIIIOBbIX MaIIHH OCHOBaHa Ha y6eJKeHnn, YTO eHeprHa, IIOBeIeHHa K MaIIHN He B yIIOpaIIOeHHo fOpMe, MoKet 6bITb IeJIHKOM IIpeBpaIeHa B IIO6oIpyToe eBnI[9].OTcIOda -IeJIeHne BCEx fOpM eHeprHa H aHmponuInbIe H 6e3HmponuInbIe [36]. OTroIOckn TaKOrO IeJIeHHa 3Byuat B yTBepKJeHHx O HeIIpHMeHHMOCTn2-TO 3aKoHa TepMOIHnAMHKN (IIpHHIIHa NCKJIIOueHHoro BeUHO TBnIaTeJIa 2-TO poJa) K HETeIIIObbIM MaIIINHAM, a TaKKeB HeO6OCHOBaHHbIX yIIpeKax B aIpcSec TEIIIOBbIX 3JIeKTprHuecknx CTAHIIIN (T3C) B <PaTcOHTeJIbCTBe> HMN 6OIbIeI qactN TeIIIObTI cTropAHN ToIIINBa. IIpn 3tOM B HayHoN I OKIoHOayHoo JInTEpaType peIKO cJIbIIaTcra RoIoca Tex, KTO IOHMaET IIpuHHy TaKo pa3HOroIOChIbMIHeHNI. MeKdy Tem OHa JLeKH T IIpHMeHHn OHoro n Toro JKe TepMHNa KIIД K IByM IIpHHIIINIAJBHO pa3JIuHbIM TIIAm IIpeo6pa3OBAteJIe IHeRTH pa3JIuHbIM KpHTepHnMn IH 3ΦΦeKTHBHOCTn. IIOHATHE KIIJ 6bIIO BBEJeHO B Hauky N TeXHNKY B KOHcE XIX BeKa, KOrJa yKe cyUeCTBOBaJIH He ToJIbKO MExaHHueCKHe IJIeKTPnueCKHe, HO N TeIIIOBbIE MaIIINHbI. OHaKo HxKIIД OIIpeJIeJIcIpa3JIuHbIM O6pa3OM. Y MExaHHueCKN H IOIO6HbIX IM MaIIINHax, IIJRA KOTOpbIX 6bJIa H3BeCTHa He TOJIbKO COBepIIaemA HM pa6Ota W, Ho N MoIIHocTB N =dW/dt, KIIJ NOIIpeJIeJIcI cTHOIIeHNEM HX BixOJHO MOIIHOCTH N" K MOIIHOCTN Ha BX OJeN'JIH JKe OTOHIIeHNEM COBepIIaemO MAIIINHOI IOJIe3HOJ pa6OtBI W" K TeOpETNUeCKN BO3MOJHOI W" B TepMOIHAMHK TaKOrO poJa KIIJ Ha3bIbAIOTc oMhOCumeJIbHbIMu. IHaYe OIIpeJIeJIeTcR «TePMHueCKN» KIIJ TELIOBOJ MaIIINHBIn, OTHOCJIINcR K pa3Pryd a6coIOMhIX. B IIKJIuVEckNX TEIIIOBbIX MaIIINHax, rIe HapJy C HCTOCHNKOM TEIIJa Q1Heo6XoDNM TELIOIPnEHmHIke Q2, OH OIIpeJIeTcR OTHIOIIeHNEMIOJIe3HOJ pa6OtbI W" K IOIDBeIJHHOI OT Ropayero HCTOCHNka TEIIIOTeQ1H 3aBNCHT OT cpeIHHX TEIIIepaTyp pa6OyeRO TeJa yCTaHOBKNB IpoIeCEe IIOIBOda IOTBOJa TEIIJa $\overline{\mathbb{T}}_1$ n $\overline{\mathbb{T}}_2$ [37]: $$ \eta_ {\mathrm {t}} \equiv \mathrm {W} / \mathrm {Q} _ {1} = 1 - \bar {\mathrm {T}} _ {2} / \bar {\mathrm {T}} _ {1} < 1, \tag {19} $$ 3TN KIIJ XapaKTePn3yIOT cmeneH npebpamuMocmu TEIIIOBOI 3HePHH, IIOBDOHMo K TeIIIOBOIMaIIINHe. TaKOro poJa a6coJIIOTHbIe KII MoYr 6bITb OIIpeJeJIeHbI JIA JIO6Oi FOpMbI 3HePHH, IIOBDOHMo K IIpeo6pa3OBaTEJIHO 3HePHH BO3JEcTBHEm, OIIHCbIBaEMbIM 1- h cyMMo ToKJDECtBa(9). IIph TaKOM IOXoIDEcTBeHHbIM o6pa3OM BO3HNkaET IIpeJCTaBJIeHne O eINHCTBE BbIPaJKeHHa 6coJIOTHO R KIIJ TEEIIIOBOI HJIN HeTeIIIOBOI INKJIINCeCKoMaIIINbI KaK o6 OTHOIIeHHCOBepIIaEMo B IINKJIe IIOIE3HO pa6OtBI Wk IIOCTyIIaIOIIe Ha BXoJ MaIIINHbI 3HePHH U. 3TOr KIIJDyIO6HO BbIPA3HTb Ype3 cpeIHHe IOTEHIIHaJIbI 3HePROHOCHTeJIa$\Theta_{\mathrm{i}}$B IIpoIeccax erO BXoJ H BbIXoJ H3 yctAHOBKN$\Psi_{1}$n$\Psi_{2}$KaK aHaJIIOBcpeJHEtePMoIHHa MnueckoI TeMIIepaTybI IIOB0da H OTBOJa TeIIJa $\overline{\mathbf{T}}_1 = \Delta \mathbf{S}_1$ $^1\int T_1\mathrm{d}S_1\mathrm{H}\overline{T}_2 = \Delta S_2^{-1}\int T_2\mathrm{d}S_2.$ Iprn 3TOM BbipajKeHne a6coJIHOrTO KIIJ JIO6Oi (IINKJIInuecKOi H NeIKJIInuecKOi) MaIIHHbI IIpHMET BnI [38]: $$ \eta_{max} = \mathrm{W}_{\mathrm{tt}} / \mathrm{E}_1 = 1 - \Psi_2 / \Psi_1. $$ TaKOBbl,HaipnMep,paCINHPteJIbHbIeMaIIHHbI (TeaHJepbl),ocyIeCTBJIHOIIne paCINHPeHHe IIOToKa ra3a OT daJIeHNp1 Do $\mathfrak{p}_2 < \mathfrak{p}_1$,MaHHTOrTHIpOIMHaMHueCKHe REhepaTOpbl,pa6oTAIOIIne IIOOTKpbITOn cXeMe C 3HTaJIbHne IIa3MbI Ha BXOe H BIXOe reHepaTopah1n h2 $< \mathrm{h}_{1}$;BeTpO3HEPReTNUeCKHe yCTaHOBKn co cKOpocTAMn Betpa Ha BXOe H BIXOe V1n V2<V1;JIeKTPOcTaTHueCKHe MaIIHHbI,IOUYaIOIIne 3apJI pIn IOTeHuaJIe 1 H OTaIOIIne erIo pIn IOTeHuaJIe 2< φ1 n T.I.Д JIg BCEx HNX abCOJIIOHTbIe KII MeHbIe eINHHbI,IOCKOIbKY abCOJIIOHTbIe 3HaueHn IIOTeHuaJIa IpnEeMHNka 3HEpRnY $\Psi_{2}$ He MOrYT b6ITb paBHbI HUIO Hn TeOpETNUeCKn (IOCKOIbKY IIPN 3TOM B3aHMOJeCTBHe C HNM cTaHOBHTcR HeBO3MOKHBIM), Hn TEM 60JIee IpaKTNUeCKN.3TO 6oCTOaTEJBCTBO CBHIETeJBCTBYet O eINHCTBE 3aKOHOB IIpeo6pa3OBAHHaJIIO6bIX fOpM 3HEpRn, a CTeIeHbIO HepaBHOBecHOCTN HcTOUHHKa IIpeo6pa3yEmoJ IIIom pa3JIuHNe I nepeo6pa3OBATeJIe Pa3JIuHbIX fOpM 3HEpRn NOppeJIAHotc He CamoJ 3TOI oFpMoJ, a CTeIeHbIO HepaBHOBecHOCTN HcTOUHHKa IIpeo6pa3yEmoJ 3HEpRn, T.e. OTHOIIeHHem pacIOJaRaEMO rpePiADaO6OIIeHHoro IOTeHuaJIa $\Psi_{\mathrm{I}}\mathrm{K}$ abCOJIIOHTHOI BeIHnuHE MmG,H, aero abCOJIIOHTHyO BeIHnuHHy H1OTcHTbIBaTBOT IeHTpa 3eIMn c paAInycom R=6·106 M.Torga e e «a6coJIIOHTbI» KIII coCTaBHT BeIHnuHHy g=△H/ H ≦5·10-6. TaKHM o6pa3OM, Mbl OyeHb DaJIekn OT BO3MOKHOCTH HCIOJIb3OBaTB «BCIO rpaBHtAUHOHHyo 3HEpRHoO», Tak YTO TEIIIOBBle MaIIHHbI - OTHOID He camble «paCTOHTeJIbHbIe» B OTHOIIeHHN HCIOJIb3OBaHHN IIOTEHIIaJIa YI ppeo6pa3yEmoJ fOpMbI 3HEpRn. EINHCTBO BbipaxeHH KII TeIIOBbIX H HETeIIIOBbIX IIKKJIInueckHX MaIIHH, BBipaKa-emoe COOTHOIIeHHem (20), IIO3BOJIaET o6OCHOBaTB IIpHIIINBI HcKIIIOUeHHoro BeuHOrO IIBnIaTeJI 1-RO n 2-RO poJa, He IIpH6eRa K IOCTyIaTAM. EcJH eHeprHg E1, IIOIboIMma K MaIIINHe, paBHa HJIIO, To corJIaIcHo (20) 6yIeT paBHa HJIIO Hpa6Ota TAKoMaIIINHbI W(1-e HaayAIO TepMOIHnHAMNK). EcJH cpeJa, IyJIaHOIIaCRA hCTOUnHKOM eHeprHg E, OIIHpOJHa, T. e. $\Psi_{1} = \Psi_{2}$, To KIIД taKoMaIIINHbM =0, KaK H ePa6OtaW. ΘTo IIOIOKeHne MoKet 6bITb o6OIIeHO H Na HeIIKNJIInueckHe MaIIINHbI [39]. ### g) OnpoBepKHeue meopuu «menlooBcmepuu BceIeHHO» IIpn 06OCHOBaHHn IIpHINHIIa BO3paCTaHHN 3HTPOIIHH P. KJIay3Hyc OCHOBbIBaJIcH Na Ka3aBIIeMcR OeBHNbIM NocTyJIaTe O TOM, YTO TepMHueckn KIIJ JIIO60I Heo6paTHMOI TeIIIOBOI MaIHHHbI $\eta_{\mathrm{t}} = 1 - Q_{2} / Q_{1}$ MeHbIe, YEM B o6paTHMOM IINKJIe KapHO $\eta_{\mathrm{t}}^{\mathrm{K}} = 1 - T_{2} / T_{1}$ IIpnI Tex JIe TMIIepaTypax TEIIIOHcTOUHHKa T H TEIIIOIIpHEMHHKa T2 H KOJIInueCTBAX IOJBeIeHHoro Q H OTBeIeHHoro Q2 TeIIIA.B TaKOM cIyae dS2= $\delta Q_2 / T_2 > dS_1 =$ $\delta Q_{1} / T_{1}$, T. e. 3HTPOIIHcHcTeMbI, BKJIIOHaOHIIe HcTOUHHK TeIIIA, IIKJIInueCKN IeIcTBYIOUIYIO TeIIIOByO MaIHHHy I TEIIIOIIpEHMHK, BO3paCTaeT. He HauB B 3TOM paccyKJdeHNN KaKHX-JH60 IipOTHBopeuH, P. KJIay3Hyc IIpHJaI 3TOMy BbIBOy cTaTyC oIIeΦH3HueCKOrO «IPHHINIIa BO3paCTaHnN 3HTPOINH» I IOJIOHN I eO B OCHOBY «TeOpH N TeIIIOBOc MepTH BceJIeHNoI>. 3Ta TeOpH IpeIcka3bIBaJIa IIpeKpaIeHne BO B CeJIeHNoB B IeIOM KaKHX-JH60 MaKpOIIpoIeCCOB BCIEcTBHe HAcTyIJIeHnB H He TepMOINHAMueCKOro paBHOBecn, YTO 6blIO paBHOCHJBHO yTBepKJdeHNo O eE «COTBOPHMocTHN). 3Ta TeOpH IIO cNX Iop He OIIPOBeprHyta HecMOTpy Ha To, YTO yHOMaHyTae «TeIIIOBa CMEtB» He HAcTyIINJa H ueP3 13-14 MHIJIInapIOB Jiet, OTNyIeHHbIX eN 3TOn MoJeJIbHO. MeKJy TeM B paccyKJdeHn KJIay3Hyca BkpaJIacb OIIIN6ka, He 3aMeueHHa Hn erO COBpeMeHHKaMn, HN IIOJIeIOBaTeJIaMH. OHa cTaHet 6OIee OYeBHJHOH, ecJIH NcIIIOJIb3OBaTb BbIPAKeHHe (11),coRIaCHO KOtOpOMY IIpH OINHX H Tex Jke T1H T2 KIIД o6paTHMoH IN Heo6paTHMOI TeIIIOBOH MaIIHHbI OINHaKObBI. CJIeIOBaTeJIbHO, OIIIN6ka KJIay3NuCA coCTOJIa B yTBePKeHHN, YTO cpaBHNBaEMbIe MaIIHHbI HMeJIH OINHaKObIe TeMIpeaTypbI rOpJeHO IN XOJIIOHO R HCTOUYHKOB. CTOJIb JKe HECOCOTeJIbHbIMN Oka3bIBaOTcH Ha IIOBepKy IpyrHe JOKa3aTeJIbCtBA 3TOTO IIpHHIIHa [40]. BoJee TOrO, MoKHO IIOKa3aTb, YTO, ocTaBaJcB PamKaX paBHObecHOI TePMoINHAMNK, JOKa3aTb IIpHHIIBO3paCTaHnH 3HTPOIIHH BO6Ue HeBO3MOxHO. JIAI 3TOTO IOCTaTOUHO paccMOTpeTB cHCTeMy, BHYTpEHnH 3HePTHN KToTopo UOnpeJIeETcHHTPOIIHe S Ho6bEMOM V, T. e.U=U (S, V). ToJa, paccMaTPHBaB o6bHuBM I6pa3OM 3HTPOIIHO KaK o6paTHyIO yHKIIIO S=S (U,V), Mbl C Heo6XoIHMOCTbIO IIpNDEM K BBIOy, YTO B H3OJIInPoBAHHbIX cHCTeMax, IDe B CHNY 3aKOHOB coXpAHnH UNV, = const, 3HTPOIIHtAKKe DOLJKHa ocTaBaTcBcH Neu3MeHHoR [41]: $$ \mathrm {S} _ {\mathrm {H 3}} = \mathrm {S} (\mathrm {U}, \mathrm {V}) _ {\mathrm {H 3}} = \text {c o n s t .} \tag {21} $$ KapINHaJIbHoe peIIeHHe 3TOrO BOIIpOca IaET BBeIeHHe TepMOHNyIbCa $\Theta_{\mathrm{q}}$ KaK HCTHHoH MebpI BHyIpeHHe TEPIOBOH 3HeprHn Uq = TΘq. CoJIacHO 3Tomy BbIPAKeHHIO, TepMOHNyIbC cHCTeMbI MoKet y6bIBaTB He TOJIbKO IIpH 3aTyXaHHN KOJIe6aHH N IIpeBpaIeHHN TEIIIOBOH 3HeprHn Uq BO BHTpeHHIO IOTEHIHaJIbHyIO 3HeprHIO ToJ KcHCTeMbI Er, HO IIpH eIIpeBpaIeHHN B KInHETHueCKyIO 3HeprHIO YIOPAIOeHHORO DBHXeHHN Ew. DeIcTBHTeJIbHO, IIO Mepe IIpH6JIHKeHHN CkOPoCTn cHCTeMbIK IIpeJIbHOJ cKOpocTH pAcIPOcTpaHEHHN BO3MyIeHHN, KOrDa eIIpeBbIiEHHNE B KOJIe6aTeJIbHOM IIpoIeCE cTAHOBHTC HeBO3MOKHBIM, 3TOT IIpoIeCC IIpeKpaIIaeTcR, T. e. TEIIIOBoE (HeyIopAIOueHHoe) IBDHXeHHne BbIPoKJaTeCra. IMeHHO IIOT IIpNHHe TEMIIpePAtypaTn H3JIyUeHHN HJIN fH3NueCKOTo BaKyyMa, B KOToPbIX cKOpocTb CBeTa MaKcMJaJIbHa, paBHa HUHO. CJIeIOBaTeJIbHO, TepMOHmIIyJbC bIbPoJdaeTcH II pRn B3pblBe $\ll$ CBepXHObIX》, COIIpoBOJdaIOIHMCs IpeBpaIeHNHe BIECTBa B H3JIyueHHe. 3TOI IpoIeCC MoKeT cIJyKHTb IIpHMepOM BO3HHKHOBeHHN $\ll$ IopraKa> H3 $\ll$ XaOca>, BO3MOJxOcTb KToPOrO o6oCHOBaI I. IIpHiroKHH [27]. Tem caMbIM 3aMeHa 3HTPOIIHH TepMOHMIyJBcOM ycTpaHReT HabJ3aHHyIO TepMOdINHaMHKOJ KJIay3HyCa OJHOCTOPOHHIO HO HAIIpaBIeHHOCtB IIpoIeCCOB BO BCEJIeHHo, IOnyckA Bo3MOJxHOCtB eE HeORpaHHYeHHOrO BO BpeMeHH II pOcTpaHcTBe fYHKUHOHnpOBaHHa, MHHyacOCTOAHne paBHOBecHn. ### h) YcmpaHene napadokca Fu66ca CpeHn IapaIOKOB fH3KN HbA JIN HauJIETcE Ie OINH cTOLJ KHe H3BeCTHbI H cTOLJ KHe 3aRaIOUHbI, KaK «IpaIOKc Tn66ca» -ytBepKJDeHne O cKauKoo6pa3HOM BO3pactAHHH 3HTPOIIHH IIPN CMeIIIEHHN HE3aHMOJeCTBByIOIHX INeAJIbHBIX Ra3OB B OTCyTcTBHe KaKHx-JIN60 TeIIIOBbIX INI IOBEMbIX 3ΦΦeKTOB. B CBOe 3HaMeHHTO pa6OTE «O paBHOBecHN rTepeRrHbIX BeIeCTB》 [42] Jk. Tn66c pacIpoocTpahn MeToDBI TepMOHNAMHK 3aKpbBTbIX CnCTEm, IIpeIcTaNB HX KaK COBOKYIIHOCTb OTKpBTbIX CnCTEm, pa3JeIeHHbIX ycIOBHBMn IIOJyIIPOHIIaeMbIM NpeEROpDKAMn. Tem CAMbIM OH 3aMeHNJI BHYtpeHHHe IPOIeCCbI H3MeHeHHa COCTaBA ChCTeMbI IPOIeCCaMn BHeIIHeRo H36HpateJIbHOrO MaccOO6MeHa (INΦΦy3HN Ype3 rpaHHbI IOIChCTeM). IIpn OTOM OH 06hApjKJI, YTO pa3HOctb Mekdy 3HTPOIIHe CMecn IByx Macc INeAJIbHBIX Ra3OB M1 H M2, KaKDbI H3 KOToPbIX 3aHmAJI BNaJaJI IIOJOBNHy IIOJHOo 6bEMacMeCN V, 6oJIbIIe cyMMbI 3HTPOIIH tex Jhe Ra3OB Do CMeIIeHHa NaIOCTOARHHY BoJIuHHy $$ \Delta S_{\mathrm{cM}} = R_{\mathrm{c}} \ln 2, $$ OπpeIeJIaEMyH NCKJIIOUHTeJIbHO Ra3OBOIIOCTOAHHO cmecnRc. XapaKTePHo, YTo caM Γn66c, oChOBbIbAcb Ha cTaTHCTUWeCKo HHTepPpeTaUHH 3HTpOIIHH, He yCmTaPbHbJI B 3TOM pe3yJIbTaTe HnueFo IapAoKcaJIbHOro, CHTaJ, YTO OH «BceIeJIO OIIpeJeJIeTcYHCJOM CMeIIINBaEMbIX MOIEKUYI» N 3aBNCHT JInIIIb OT TOGO, CHTaEIM JIN MBI HX TOKeCTBeHHbIMN HIn pa3DnHMBIMN. OHaKO No Mepe H3yUHeH NTO BOIIPOca HCCJIeIOBaTEIJ HAtaJIKNBaJIHcB Ha BCE 6OJIbIIHe N 6OJIbIIHe TpydHocTH, YTO N obycIOBNIIO IOABJIeHne CJIOBOcoOeTaHHA «IpaIoKc Γn66ca>. B TeueHne IIOJyTopa CToJIeTHAToT pe3yIbTaT He pa3 cTaHOBnIcra O6BeKToM HCCJIeIOBaHnKaK ΦH3NKOB, TaK HΦHIOcoΦOB. MHorHM erO HccJIeIOBaTeJAM Ka3aIOocb, YTO OHN cyMeJIN, HaKOHeII, O6bAcHNTb CTpaHHyO He3aBnCHMOCTb cKaUka 3HTPOIIHH OT cTeIIeHN H xapaKTepa pa3JIHcYRAEMbIX rA3OB HApIy C HeOIOYCTHMOCtBu YIOMaHYTOrO cKaUkaIIpH CMeIIeHN ToXJDeCTBeHHbIX rA3OB. Ondako IIOIO6Ho JIeEHdApHomy CΦHHKcy 3TOT IAPAIOKC BHOb N BHOb BO3HnKaJI Ha CTpaHHaX HayhBix KHN I JxypHaIOB H He COIIeJI C HNX BIIOb Do HAcTOnIeero BpeMeHN. B HTORE 60JIbIHINcTBO HCCJIeIOBaTeJIeI ΘTOrO IAPAДOKca CKJIOHHIOcb K MHeHHIO, YTO OH «He pa3peIIHM B IIIOCKOCTN KJIacCHYeCKoI TePMoINHAMIKN» [45]. HNaYe 06ToHT JeIo, ecJIN BMeCTo 3HTpOIIHH, HMeHOIe KOnHfrypaIHouHHyIO COCTaBJIAIOUIYIO, HCIOJIb3OBaTb TepMOHMIIyJBcOq, o6JIaIOIIIN IIpocTBIM $\phi$ H3NueCKM CMBICJOM. TorJa cTaHOBHTc8 OyeBHINbIM, YTO IIpi CMeIIIBaHH N HeB3aHMOJeICTByIOIIHX Ra3OB C OINHaKOBOI TeMIIEpaTyPoR H daBJIeHHEm TepMOHMIIyJBc HE MeHReTcXOT8 6bI B cHIy 3aKoHa COxPaHeHHN HMIyIJbc CaHCTeMbI B IEJIOM. 3TO TEM 6OJIee OyeBnIO, YTO oBa r3a eIIe IIO CMeIIeHHN HaXODJIINcB B TepMHueCKOM H 6apHueCKOM paBHOBEcHH, JBJIHOIIeMcI JIa CNCTeMbI C IByM CTeIIeHAMN CBO6Obl IIOJIHBIM. ### i) YcmpaheHue npomubopeu mepMoUHaMuKc meopueu 360.1ouuu I3BecTHO<BOHIOIIepe HPOTNBOPEUHe TepMOHNHAMNK c TeOpHe 6HOJIOHTUeCKoI BOJIIOIHn> [27], o6ycIOBJIeHHoe TEM, yTO IprHINBO3pactaHHN eHTPOIIHH IpeIINcHbIAeT IprHpoJe JInIIb eE DeIgpaIaIIHO. BepoTHOCTHa TpaKTOBka 3HTPOIIHH BoJIbMaHOM He pa3peIIaJa 3TO IPOTNBOpeUHe, IocKOJIbKy JaBaJa BceJIeHHoJ INIIb HNUToKHbI IIaHC N36eKaTb <TEIIIOBoCmepTH>. MeKJy TEM HecJIIOXHO JOKa3aTb, YTO KaKHe-JIb6o peaJIbHbIe IpoIeccbI dρi/dt≠0 MOγT BO3HHKHyTb TOJIbKO B HepaBHOBecHBIX cHCTeMax (rIe ρi≠p), a HxCKOpocTHB pa3HbIX qactyx cHCTeMbI 3JIeMeHTax o6bE Ma dVHMeOT IpoTHBOIOJIOJKHbI 3HaK. B 3TOM JIeTKO y6eINITbc8, IpeIcTaHB JIO60 EKCTeHCNBHI IIpaAMTp HeOIHOPoIHoH cHCTeMbI Θi (eē MaccyM, YHcIIO MOJIeK-XBEIIeCTB Nk, 3HTpOIIHOS, 3JIeKtpNueckn 3apJ3, HMIyJIbc P, ero MOMeHT L n.T.П.) HHTerpaIOM OT eRO JIOKaJIbHOHρi = dΘi/dV IN cpeIHeH Oρi = Θi/V IIIOTHOCTH BbIPaJKeHNem Θi = ∫ρi dV= ∫ρi dV.ToIgda $$ \int \left[ \left( d \left( \rho_{i} - \bar{\rho}_{i} \right) / d t \right) \right] d V \equiv 0. $$ JERKO BnIeTb, YTO 3TO TOKJeCTBO BBIIIOJIHReTcB TOJIbKO B TOM cJIyae, KOrJa IIpoIeCCbI d(ρi - Pj)/dt IIpoTHBOHaIIpaBJIeHbI. 3TO IIOLOKeHHe, Ha3BaHHoe HAMN «npununom npomu6o-Hanpa6JIeHNOCMu npouecco6», MoKeT paccMaTpNBaTbcK KaK MaTeMaTHueCKoe BbIPAkeHne JINAJeKTHueCKOTo 3aKOHa «EINHCTBa N 6Opb6bl IIPOTHBOIOJIOXHOCTeR>. 3BpHCTNUeCKaI IeHHOCbT 3TOrO IIINHIHa KaK OJHOrO H3 HAn6OJIee 06IIHX 3aKOHOB ECTcTB03HAHHcCtOHT B 06HApUKeHHn CInEIHΦHueCKOTo KJIacca IIpoIeCCOB «noJrpU3auu» CnCTeMbl B CaMOM 06IeM IOHNMaHH 3TOrO TepMHHa KaK IIOBJIeHHa B HeJ YAcTeI (06JIaCTeI, φa3, KOMIOHErTOB) C IIPOTHBOIOJIOKHbIMN CBOICTBaMH. TOT IIHHHII ycTpaHye HAIB3aHHyTOpeMOHNAMHKo KJIay3Hyca OINocTopoHHIOHaIIpaBJIeHHocTB IpoIeCCOB BO BceJIeHHoJ. K TaKOMy JKeBBIOy MBI IIpHXOIM, 6a3Hpyacb Ha 3aKOHe coXpaHeHHN3HePHH B H3OJIHpOBaHHoC nCTeme $(\mathrm{dU / dt})_{\mathrm{H3}} = 0$ H TOKJIecTBe (10), ecIII IpeIcTaBHM $\mathbf{F_i}\cdot \mathbf{v_i}$ B BVHeI IPOIN3BeIeHnna CNI I NIOToKOB $\mathrm{X_i}:\mathrm{J_i}$ KaK 3TO IpiHnTo B HepaBHObecHO TepMOHNHaMHKe [11-14].IIOckOJIbky JKe B H3OJIHpOBaHHbIX cHCTeMAX H3MeHEne IIapAmTePob O6yCIOBJIeHo NCKIIOUHTeJIbHO HaJIINuHem y HNX BHYTrpeHHNX HcTOUYHHKOB, TO IpOTNBOIOLOJXnB 3NaK HMeOT H MOIHOCTHN $\mathrm{X_i}:\mathrm{J_iPa3HOIMEHHbIX}$ IPOIeCCOB IpeBpaIeHnA 3HePnn. 3TO O3HaueT, YTO HApA dy C IPOIeCCAM NHCCIIaIIHN, B KOTOpbIX $\mathrm{X_i}:\mathrm{J_i}>$ 0, B H3OJIHpOBaHHbIX cHCTeMax HeN36eJHbI I IPOIeCCsI «CaMoOpraHH3aIIHN» HEKOTopbIX j-X CTeJIeHn CBO6OJIbI, B KOTOpbIX IPOIN3BeIeHnE $\mathrm{X_j}:\mathrm{J_j}<$ 0. TaKOBi, B YacTHoCTn, IPOIeCCsI «BOcXoJIaIIeI INΦΦy3HN» (IpepeHocBa BeIEcTBa B cTOpOHy BO3pacTaHnE rO KOHIeHTpaIHN), JABJIeHnA «COIIpJKeHnA» XHMUeCKHX peAKIIIN (IPOTekaHnpeAKIIIN B HAIIpaBJIeHn BO3pacTaHn E e cPoIcTBA), «AKTHBHOrTO pAnCIOptA» (HakONJIeHnB OprAHx BeIEcTBc 6OJIbIIe IHeR Nei ΓNo65ca) n T.I. TaKM O6pa3OM B HepaBHObecHBx cHCTeMax C Heo6XoINMOCTbIO BO3HNKaOT IPOITHBOHaIIpaBJIeHHbI IPOIeCCsI 3BOJIIOHN HNBOLIOIIIN (JePaJaIIIN), KOrDa OJHa CTeJIeHb CBO6OJIbI cHCTeMbl IpoTHBOpeHuTEPMODINHAMNKc 3BOJIIOIIIn. BoJee TOrO, ToKJecTBo (10) coJepKHT TepMOHNHaMnueckHne cHJIbI, BbIPAkaemblie rpaJIneHTaMH IOTeHINaJa Xi= Vψi, H3MeHeHne KOTOpbIX OtpaKaET 6e3 IIOIOJIHNTeJIbHbIX paChETOB He TOJIbKO IIpH6JIINKeHne HJIN ydaJIeHne cHCTeMbI OT COCToHn paBHOBecnI IO JIO6oI i- iCTeHEn eCBO6OJBIB OTJeJIbHoCTH, HO I YcJOBHe paBHOBecnI DaHHOro poJa: $$ \mathrm{d X} _ {\mathrm{i}} > 0 \left(\text{э ＂ BOJINOIINIA}\right); \mathrm{d X} _ {\mathrm{i}} = 0 \left(\text{paBHOBeche}\right); \mathrm{d X} _ {\mathrm{i}} < 0 \left(\text{HHBOJINOIINIA}\right). \tag{23} $$ 3To DaET B pyKN HccJIeIOBaTeJIe 60JIee HaJIaIbHbI, 60JIee «Φn3UHbI» H 60JIe HnΦopMaTHBbI INcTpymeHT aHaJIIN3a Ipo6JIe MBOJIOHN, HeKeJIn He IIOJaIOIIINsCBbYHCJIeEHNO MaKChMym 3HTPOIIIN [44, 45]. IIp H 3TOM BbIaCHraETcRA, YTO Do TEX IOP, IOKa B cHCTeMe IpoTEKaIOT KaKHe-JIN6o IpoIeCCbI, CpeIN HNX O63aTeJIbHO 6yUT HMeOIIINe 3BOJIOIOHOHHbIX XapaKTep. Te CMbIM yTBepKJaAetcRA, YTO IIpyOJe CBOIcTBHeHbI He TOJIbKO pa3pyIITeJIbHbIe, HO n Co3NdaTeJIbHbIe TeHdEHIIN. 3To H Na6JIIOaETcBA KHBOn H HeKHBOn IIpyOJe Ha BCEx yPoBHx MHPo3JaHHa. j) YcmpaHene Hue npadokca ompuameIbHbIX abcoIomHbIXmemnepamyp. IIOHATHe OTRHnAteJIbHOJ a6cOJIHTHOJ (cIIHHOBoJ) TeMIIePaTpybI BO3HNKJIO BO BTOPOJ IIOIOBHe XX B IIOcJIe OTKpbITNcIINHOBbIX CnCTeM, B KOTOpBX C IIOMOIIbHO 06paIeHnI 3HaKa MaTHHTHOI IOJIa HJIN BbICOKOAcTOTHOI HmIIyIbCa YdaBaJIocb CO3JaTb «IHHBepCnIO 3aceJIeHHOCTeB> 3HEpReTIueckHX yPobHei 06JIaIAOIIHx CIIHHOM 3JIeMeHTapHbIX YacTHII -coCTOAHHe, B KOTOpBX 6OJIbIIIHCTBO 3JIeMeHTapHbIX YacTHII HaXODHTcRA Ha BepXHem 3HEpReTIueckOM yPobHe [46]. OchOBaHHem JII BBeJHn ETOI IOHHTN IIOJIyJHKJIa BCE Ta JKe CtATNCTHUeCKa TpaKTOBKa IIOHHTN 3HTPOINH. EcJIn CtATNCTHUeCKyIO 3HTPOINHO IIpHHTb TOJDECtBEHHoTepMOIHHAMHueCKoHa TOM OCHOBAHNN, YTO O6e BeJIuHNbI aDINTHBHbI NIOCTHraOT MaKcHMyMa B COCTOAHNN paBHOBecn (IpiHHIINI BoJIbMaHa), To, COIOCTaBJIA BbIPAJKeHHe IPOH3BOIDHO ( $\partial U / \partial S)$ JILI cTAHTCtUeCKn ONpeJIeHHoB BHYTpEHHeN 3HePTHN UN 3HTPOINH Sc H3BecTHbIM ONpeJIeHHem TepMOIHAMHueCKoT TeMIIePaTypbI TepMOMexaHHueCKo CHCTEMbl $$ \mathrm {T} \equiv (\partial \mathrm {U} / \partial \mathrm {S}) _ {\Theta}, \tag {24} $$ MOJHNO IpiHTHK 3aKJIIOHeHHO, YTO cNcTeMe JaIepHBIX CIIHHOB B COCToAHHH HHBepCHO 3aceJIeHHOCTH CJIeJyET IpiHINCaTb OTPiTaTEJIbHOe 3HaueHne a6coJIHOtHOI TeMIIEpaTpyB T $< 0$ XapaKTepHO, YTO IpiN TaKoI $\langle \Pi \Omega \Gamma \Omega \mathrm{H}K\rangle$ IOI KJIacCHKY> IpiHIIOsc BOIyCHTb, YTO cOCToAHHH CIIHHOBbIX CnCTem C OTPiTaTEJIbHOi a6coJIHOtHOI TeMIIEpaTpoB B HNX JIeKaT... BBIIe 6eCKOHeH O HBICOKHX TeMIIEpaTyp T $= \infty!$ CJIeIyET OTMeTHTb, YTO cyIeCTBOBaHHe cHCTEm C HHBepcHOb 3aceJIeHHocTbIO yPOBHe JYBJeTcB B HAcToJiee BpeM TBePdo yCTaHOBJeHHbIM $\phi$ aKTOM. IEPBoI IOChCTeMOI, yIOBJeTBOpHBIIeN 3THM Tpe6oBAHNm, YBHJIacb yIOMaHyTaB bIIIe cHCTeMa JIePbIX CINHOB HOHOB JIHTnB KpHcTaJIiAx $\phi$ TOHJa IINTn (LiF). EcIn KpHcTaJIbLi LiF IOMecTNTB B MaHHTHOE I0JIe, a 3aTeM 6bICtPo H3MeHHTb HaIpaBJIeHne BHeIIHeRo IIOJIa (Kak 3TO 6bIO B OIIbITax E. IpapceJa n P. IIayHa, 1951), To JaepHbIe MaHHTb OKa3bIBaOTc HecIOco6HbIMN IOCJIeOBAtB 3a HHM, N 6 JbIIaAHX qactb OKaKeTcB V BepxHEM 3HepReTHUeCKOM COCTOHHN - IPOH3OJET INHBepcHra 3aceJIeHHocTH.N TaKHX yCTaHOBkax, KaK Ja3epbl, OHa CO3JaEtcR «IOKaauKoi» IN X HeprHei MHKpOBJIHOBOrO H3JIyueHnna, 6laFoapra Yemy co3JaEtc r CTaIHohApHoe HepaBHOBeCHoe COCTOAHHe cHCTeMbI. MaTHHTHOM IOJIe, BXOJIIaB B rAMHJIbTOHHaN cHCTEmbI Hapayc 3HeprnEi CINH-CINHOBO R3aHMOJeCTBH. BHyTpeHNHa JKe 3Heprn CnCTEmu U, KOtOpa IIO nppeJeHNIO He 3aBNCHT O TIOLOXeHNr CnCTEmbI KaK IeIoro BO BHEIHINX IOJAX, OCTaBaJIacb IIpH 3TOM HEn3MeHHoB. B IpOTNBHom cIyae (Ipiu N3MeHeHNU) HApYIIaIOcb 6bl YcIOBHe IocToHCTBa B bBypaJKeHN (16) KoOpDHHaT BceX BnIOB pa60tBi, a He ToJIbKO o6bEma. 3To Kacaetc H npYrOro cIIOc6a HHBepcH NaceJIeHHocTH, IOCTHraeMOrO c IIOMOIIbO BBICOKoyactOTHOr (180- rpaIycHOrO) HmIpyIbca. 3To Bo3JeHCTBHe HNKaK HeJIb3A OTHeCTN K KaTeRopHN TeIIIOOOMeHa, IIOCKOJIbKY OHO TaK Je HMeET HaIPaBJIeHHbI XapaKTep N COOTBeTCTByeT aHaHa6aTHueckOMy IpoIeCCy COBepHIeHNHaI cHCTeMoB BHeIHHe pa60tBi. IHTeppeTaun yHOMaHybIX 3KcIIepHMeHTOB I3MeHaeTc,ecHN BMeCTo 3HTPOINBBbIPAJKeHH (16) $\Phi$ Hrpypye TepMOHMnYlbq, KOTOpBn, KaN MoUJIb cKopocTH V, He MeHaeT 3HaKa IIpN INHBepCnH MaHHTHO rIOJI. IIpn OToM cpa3y o6paIaEaTe Ha ce6y BHNMaHHe HApUIIeHne IIpHHIIHpa3JIuHNMocTH IpoIeCCOB. 3TO HApUIIeHne COCTOHT B TOM, YTO HHTeppeTAUNo 6HapUKeHHORO B 3KcIIepHMeHTe OC6oRo, KaueCTBeHHO OTJInHMOrO H HecBOIHMOrO K JpyTm IPOIeCCA CINHPeIeTOHOb peJaKcaIHH KAK TEJIIOo6MeHa. To 06CToRteJIbCTBO, YTO MeKJy TEJIIOBOJ φOpMO NIBJKeHHN H opHEtAUnHe CINHOB cyIeCTByET HEKOTOPa C8I3b, eIIe He Daet OCHOBAHNI IIpHHNCbIBaTB 3Tu φOpMy CINHOBOJ cHCTeme. H3BeCTHO, HAnPIMep, YTO OXJIaJxDeHne KOHNHeHCnpOBaHHbIX cpeI IIpaKTNUeCKN Do a6COJIHOTHO RJIY TeMIIEPaTYP He IIpHBODHT K NcYe3HOBeHHIO CO6CTBeHHORO MOMENTA BpaIeHHIAep.B TaKOM cIyuae OCHOBaHHI DJIa Tp KAOBKn TEMIIeptyp bIT KaK OTPHAteJIbHOH, He ocTaETc. 3TN 3KcIIepHMeHTb IIOITBepINI (c IIpHemJIeMoTOUHOCTbIO) cIIpaBeJINBOcTb 3aKOHa coXpaHeHHMOMeHTa KOJIInueCTBa IIBHXeHN Iprn CIIHH-CIIHHOBMO B3aHMOJeCTBHN IIOKa3aJIH, YTO «TeMIpeaTypa» cMecnOIIpeJIeTcR bIpaJKeHHEm: $$ T = (\Sigma_i C_i / T_i) / \Sigma_i C_i, $$ T - TemIIepaTypa KaKo-JIH6O YacTH cIHHOBocHCTeMbI; $C_i$ - BecOBO Ko3ΦΦHnHeHT, Ha3BaHHbIKcIIepHMeHTaTopaMH «CIINHOBOI TEIIIOeMKocTBIO>.KaCJIeIyET H3 BbIPAKeHNr (23),B HeM CO «CIINHOBOITeIIIOeMKocTBIO» $C_i$ coPRAKeHa BeJINuHHa, 06paTHaABCOJIHOHOr TemIIepaType.TaKHM o6pa3OM,peYb B 3THXOKcIIepHMeHTax IIdet BOBce He O TepMOJINHaMHueckOITemIIepaType,a O HeKOe CtATNCTHueckOM IapAMeTpepacPiPeJeJIeHNr,BbIaBAEMOM 3a HeE. ### k) IckloueHue «uHbepcuu» 2-20 haqua mepmouhamuku BBeIeHHe IIOHHTN OTrnHaTeJIbHOJ a6COJIHOH TeMIIepaTpyb, K coKaJIeHNIO, He orpaHnUJIncb HHBepcHeI IIkaJIbI TeMIIepaTp. IocJIeIOBaJI HeH36eKHbI BbIBOJ 6b «HHBepcHH» B TaKHX cHCTeMaX n caMOrO IIpHnIHnIa NckJIIOueHHORo BeuHOrO IBNrAteJI 2-ro poJa [46]. Θta 《HHBepcn》 COCTOHT B yTBepKJdeHNN BO3MOJHOCTN IIJIHOro IIpeBpaIeHNN B TaKHX CnCTeMaX TEIIOTbIB pa60Ty H HeBO3MOJHOCTN, HApPoTHNB, IIOJIHOro IIpeBpaIeHNN pa60Ty. DeIcTBNTeJIbHO, IIO PamceIo, ropAumB b OJIaCTN T<0 cJIeIyET cHITaTb TEIo c 6oJIbIeH TeIIePAtypoR (T. e. c MeHbIeH IIO a6COJIHOH BoJIuHHe OTPiIaTeJIbHO TEmIIePAtypoR). EIN TeIepb IIpeIcTaBHTb ce6e IIKJI KapHo, ocyIeCTBJIaEMbI Iprn OToPIaTeJIbHbIX TeIIePAtypax rOpAeero H XoJIoIHOrO TeI T1 n T2, TO TepMueckn KII d O6paTHMoM MaIIINbI KapHo $\eta_{\mathrm{t}}^{\mathrm{K}} = 1 - \mathrm{T}_{2} / \mathrm{T}_{1}$ cTaHET OTPiAteJIbHbIM, IIOCKOJIbKY rOpAumB b OJIaCTN T < 0 cJIeIyET cHITaTb TEIo c MeHbIeH IIO a6coJIHOH BeJIuHHe OTPiAteJIbHO TEmIIePAtypoR $(\mathrm{T}_2 / \mathrm{T}_1 > 1)$ [9]. ΘTOr 6OIe Yem «YdHBNTeJIbHbI» pe3yIbTat O3NaHaet, YTO COBepIIaEmaR B 3TOI OBIaCtN TemIIePAtyp pa60ra IIKJIa KapHo 6UET IIOLOKHTeJIbHO, ecIn TEIIIO Q2 OTbPaEtCRAOT «XoIOJHO» HcTOHNka, a TEIIIOIIpHEMNKOM JABIAETCBAOIE ROPaee TEJO. IIOCKOJIbKy JKe C IIOMOIIbIO TEOIIOBOr KOHTaTKaMeJy TEOIIOCTOCHHKOM H TEIIIOIIpHEMNKOM BCE TEIIIOQ $Q_{1}$ IpePeHaHHoe «TropAeMy» HcTOHNKU, MoKET 6bITb IyTeM TEIIIOOBMeHa BO3BpaISeHO «XoIOJHOMy», TO B HeIIpePBIBHO IIOCEIOBaTEJIbHOCTN IIKJIIOB pa60ra 6UET IIPOIN3BOIDTbcra 3a ChET TEIIIOBTb TOJIbKO OJHORO «XoIOJHO» TEJa 6e3 KaKx-JIN6O OCTaTOUYBX IN3MeHeH N B IpyTHX TEJIaX B HApUIIeHne 2-TO HauJaIa TepMOiINHAMNKn. Tem cambl IpeTePJIeIN «HINBPcHIO» He TOJIbKO IIOHATHE TepMOiINHAMUECKO TEmIIePAtpyk Ka BEJIuHNbI cyTu6o IIOLOKHTeJIbHO, Ho N IpiHINIII HCKIJOHEN HO TAYKO BcHIOF OBEHORO DBNrAteTLE 2-TO pQA. XapAKTeHO, YTO TakoB BBIOB 6bl CJeIaHHa OCHOBAHn...TORO JKe BTOPOrHO HcaJA! B camom Jele, BO3MOJHOCTB IOJHO TPEBpaISeHNA TEJIa B pa60ty O3NaHaet, YTO oblyHoe BbypaKeHne KIIID () He IpiPMeHMBo bOJIaCTN T < 0. Ho TOrJa, OyeBHINO, yTPaunBaIOT cHIy N BCE BBIOBIs, OCHOBAHhIE Ha HEm! HaJIIO «IIOPOUHyB Kpyr»! Tem He MeHee, yTBepKJdeHne 6«HHBepCNH> IIpiHNIIHa HCKIJOUChEHHORO BeHORO DBNrAteTIA 2-TO pOA IIpoHNKlO Ha CTpaHNbI yue6HNKOB H cTAJO BOCIPONIHBOITbcra DaJce B LiYUnHex H3 HNX. 3TO LINIIb ODNH III MHOJEcTBa IIpIMepOB TORO, KAc OTOXDeCTBJIeHNE TEPMOiINHAMueckOn H cTaTHCTNHecKOn 3HTPOIIHN IIOpBbAet 6blIyIO yBepeHHocTb B HEIOrpeIHIMOCTH TepMOiINHAMKN H HeIpeJIOJHO N cPiBaBeJDINBOcTH eCJIedCTBNI. ### i) YcmpaHeHue npadokca peJmuBucmckux meJno8bIX MaUuH B roIbI, IocJIeIOBaIIHHe 3a IOBJIeHHem$\phi$yHJaMeHTaJIbHOJ pa6OtBJ A. ΘHIIITeHa(1905), coIepKjaIBIeI φOpMyIHpOBKy cIeIINaJIbHOJ TeOpHN oTHOCHTeJIbHOCTN (CTO),$\phi$H3IKN cTpeMHJIHcB IIpHJaTaB KJIaccHueCKHM 3aKOHAM TaKO N BnI, KOTo H 6bl 6bl INHBapHaHTeH BO BCEX INHEPIIHaJIbHbIX cHCTeMax OTCyEta. B 6JIacTH TepMOINHAMKN 3TO OcyIeCTBnI BIIePBbIE M. IJIaHK B 1907 r.[47]. OH IIp HIEJI K BBIO J, YTO 3HTPOIIHsOJIkHa ocTaBaTbc JIoPeHI- INHBapHaHTHOJ, IIOCKoJIbKY ycKopeHHe cHCTeMbI OcyIeCTBJIeTcA dHa6aTHUeCKN, B TO BpeM KaK BHYTpEHNO 3HeprHIO U, TeIIOTy Q H TeMIIepaTpy T cJIeIyET Ipeo6pa3OBbIBaTB B COOTBeTCTBHH C BBIPAKeHHaMH: $$ \mathrm {U} ^ {\prime} = \mathrm {U} _ {\mathrm {o}} / \gamma ; \mathrm {Q} ^ {\prime} = \mathrm {Q} \gamma ; \mathrm {T} ^ {\prime} = \mathrm {T} \gamma , \tag {26} $$ Tge Q', T' - TeIIIOTa H TeMIIEpaTypa B cHcTeMe oTcHcTa, IINKyuIeIcra OTHOChTEJIbHO Ha6JIHOJaTeJIa CO cKOpocTbIO V; \(\gamma = (1 - v^{2} / c^{2})^{1/2} - MHOJHTeJIb JIopeHua;c - cKOpocTb CBeTa B BaKyyMe. Bp8yIbTaTe O H IIp HIIeJI K BBIOBy, YTO KIIpeJIaTHBnCTCKOrO IHKJa KaHO ONpeJIeJIaTcR BbIPAKeHHem: $$ \eta_ {t} ^ {\mathrm {K}} \equiv W _ {\mathrm {U}} ^ {\prime} / Q _ {\mathrm {r}} ^ {\prime} = 1 - T _ {2} / \mathrm {T} _ {1} \gamma . \tag {27} $$ HaJIeHHbIe IJIaHkOM COOTHOIIeHNI IOJIyHJIN OIO6peHHe A.3HHTeHa Hn y KOrO He BbIbBAJIH COMHeHHa,IOKA B 1963X.OTr [48] He o6HapyKJI a6cypHocTb 3TOrO pe3yJIbTaTa C TOUKN 3peHHa TepMOIHHAMHKn.IeNCTBNTeJIbHo,IO IIaHky TeMIIepaTypa IBHXJUIEoCg HcTOUHHKa BceJa HnKe H3MepeHHoB HHeIOBHXHON CHCTeMe OTcyeTa, H B COOTBeTcTBHN C (19) IIpeo6pa3OBaHHaMH NtKce2da MeHbue, Yem y Klaaccueecko20,a IIpH ONPeJIeHHbIXy MOKeT OKa3aTbcj DaKe ompuameIbHbM. IIO OTTu, HApnoTHB, TEIMepaTypa IBHXJUIEoCg HcTOUHHKa 6ce2da bblue, H erO MaHHa KapHo uMeem 6olee blicokui knd, Yem KIAccuueckra: $$ \eta_ {t} ^ {\mathrm{K}} _ {\left(\text{Orr}\right)} = 1 - T _ {2} \gamma / T _ {1}. \tag{28} $$ Bckope K TaKOMy JKe BbIBOdy He3aBnCmO OT X.OTTa IIpHIIeI X.Ap3eJIbc [49]. OJHaKO B OTJINHne OT OTta, OH cyeI HeIIpaBnJIbHbIMN H 0opMyJIbI Ipeo6pa3OBaHHN 3HeprHn H NMIyJIbca. Ha 3OT pa3 pa6ota 6blla 3aMeueHa, H IocJIeIOBaJIa JIaBHn HIbIKaIi, IIpHBdIIHX K OKNBJIeHHoI DnCKyCCHN Ha MExJyHapOJbIX CmHIOn3Hymax B BpIocceJIe (1968) H IIITc6ypre (1969). 3TN IINCKyCCHN 6OpayKJIn TAKoXaOC B 6BJAcTH N OIIpeJeJIeHHN 6a3OBbIX IOHArTHNI KOHIeIINr TepMOIHAMHKN, YTO X. Ap3eJIbc 3aBnJI O «COBPemEHOM KPN3Hnce TepMOIHAMHKN». I DeIO 3DeCB HE TOJIbKO B OTCYtCTBHN eDHHCTBA B peJIaTHBNCtCKHX Ipeo6pa3OBaHHX 3HeprHn, TeIIIOJbI H pa6OtBI, a 6 HeJCeJIaHUN UccIeOBeAmeI E603paUambcra K OCHOBaHUM MEPMOUnHAmUKu 6cKaui pa3, Ko2da 603NuKaem Heo6xodumocmb o6oBuHn e e Memodob Ha 6olee obuui KJIacc CuCmem. BMeCTO 3TOrO aBTOpbIMHOroUHCJIeHHBX pa6OT IIbTAJIncb «IPHMnPHTb» pa3JInHbIe Ipeo6pa3OBaHHN. IToorabHbAIhsc IaKe ITOr, YTO IIpHMHeHNE ToI HIN HHOH φOpMylI Ipeo6pa3OBaHHN 3aBNCHT OT IIOLOKeHHN TepMOMeTpA B IPOcTpaHCTBe.B pe3yJIbTaTe IIpo6JIeMa peJIaTHBNCtCKHX Ipeo6pa3OBaHHN TepMOIHAMHueckHX BeJInHH 6blla «3aMeTeHa IIOKOBep». MeKJy TeM, KaK 6bIIO IOKa3aHO HAMn[20],peJIaTHBnCTcKaa MaIIHHa KapHo IIpeIcTaBJIeT co6oikOM6HHaIIIO TeIIIOBOH N MEXaHHueCKoM MaIIHHbI,IIOlyaHOIIeHapA dy c TEIIIOToQ'KNHeTHueCKyo HePngIO AEDKH =Q'(1/γ - 1), Heo6xOIMMyo dJIa IIOJIepKaHnna ero ckopocTH.N KII TakoMaIHnBbdoJIkeH OIppeJELTbcra OTHOIIeHNem cyMMapHO pa6OTbK cyMMapHOMy JKe KOJIInueCTBy IOJBeJcHNO K HeMy TEJIIOBOQ YmexaHHueckoEKNH3HeprHn.3ToT KIII IINHMaeIT IpomExkyTOUHoe 3NaueHne MeKJy ChcTO TEJIIOBOH N HcTO MEXaHHuecko MaIHnHbI H IpePxOJNT B KJIacCHueckne BbipaxeHn Hx abCoJIIOHTbIX KIII IIO Mepe H3MeHeHn HX DoJH B IIPOIN3BOJNTeJIbHOCTN KOM6HHnpOBaHHoM MaIHnHbI. OHaKo cAmIo Ce6e 3TO He peIIaET Ipo6JIeMbI peJIaTHBNCtCKHX IIpeo6pa3OBaHH TePMoIHHAMuueckNX BeJIuHH. 3Decb Ha IOMOUIB BHOBb IIPHXOJNT IOHATNE TepMOHNYJbCa KaK fHyHKINN KOJIInueCTBa DIBHXeHnR. B OTJIuHne OT 3HTpOHH, OH H3MeHJeTcR co CkOpocTbIO, B TO BpeM KaK BHYTpEHHaTeJIIOBAJHEPGRNuqHaIpoTHB, ocTaEtCRA Hen3MeHHoI IIO ONpeJeHnIO. TorJa IH X KIID ocTaEtCRA HHBapHaHTbIM IIO OTHOIIeHHIO K JIO6bIM IIpeo6pa3OBaHHM 3HTpOHH n a6coJIIOTHOH TeMIpeaTypbI [20]. ## IV. 3aklnueyne. YtpaTe TepMOHAMHKoCtAtyCa TeOpHH, bH cJIeCTBnH HocHJIN XapaKTepeJIIOXhBX NCTHH, obycIIOBJeH hIIOJIb3OBAHHem 3HTPOIIHH B HeCBOHcTBHeHHo eI POJH HocHTeJIa TEIIIOBoI OopMbI 3HeprHH. ByUyn OHIN6OuHO BBedeEHNO P. KJIy3Hycom B KaueCTBe KOOPINHaTbI TeIIIOOOMeHa, 3HTPOIIHHIOPOIDJa pRi IHEoYeBHINbIX IIpoTHBOpeChN, YNCJO KOTOpBX MHOxHIOcB IIO Mepe pacIHHPENHg OBlaCTH eE IIIOLOKeHHa. Ka IOKa3aHO B CtaTbe, ycTpaHHTb 3TN IAPAJIOTHNMbl N3 TepMOHAMHK MoKHO JINIIIb IIyTeM 3aMeHbI 3HTPOIIHH 6OJIee aDEKBaTHbIM, ObIIHM N fHI3HueCKN IIpO3paHbIM IIOHATHEm TepMOHMIyJBca. 3TO IIIO3BOJIeT He TOJIbKO UcTpaHHTb H3BeCTHBie H BHOBb 6HApuyKeHHbIE IAPAJIOTHNMbl TepMOHAMHKN H BepHYb EBI IOJIOc TcTAUC 6eRIIOte3HOI TeOpHH, HO H OTpbIBaET BO3MOXHOCTb 06BeINHeHH paBHOBeCHOH H HepaBHOBecHOI TepMOHAMHKN H HX CnHTe3a C dpyHMN fYHdAmENTaJIbHBIM INCIIINIHAMn Ha eINIHOI IOHATNIHOI H KOHIeTIyAJIbHOI OCHOBE c yUeTOM Heo6paTHMOCTH peaJIbHBIX IIpoIeCCOB. IIpn 3TOM ycTpahJeTcR «BOIIHOIIeepOTOBopeHne» TepMOHAMHKN C TeOpHeB 6HOJIOHueCKO H KOCMOJIOHueCKO 3BOJIIOHN H cyIeCTBeHHO yIpOoiaeTcR IIpeIODaBaHHe 3ToI JINCSIIINHHbI IyTeM COBepIIIEHCTBOBaHH MeTOIOB aHaJIIN3a, ycTpaeHHN TepMOHAMHCueKHX HepaBeHCTB, CTpOro JOKa3aTeJIbCTBa BCEX eIIOJOKeHH, OTKa3a OT H3JIOKeHH TepMOHAMHKn Ha OCHOBE IOCTUInPyEmbIX «HauaJI» H T. II.[50].

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