Comment on Is Tsallis Thermodynamics Nonextensive by E. Vives and A. Planes [cond-mat0106428]
Commenton“IsTsallisThermodynamicsNonextensive?”byE.VivesandA.Planes
[cond-mat/0106428]
VladimirGarc´ a-Morales andJavierCervera
DepartmentofThermodynamics,UniversityofValencia,E-46100Burjassot,Spain
Oct 2003
Wecommentonletter“IsTsallisThermodynamicsNonextensive?”byE.VivesandA.Planes
[Phys.Rev.Lett.88,020601(2002)cond-mat/0106428].ItispointedoutthattheEulerandGibbs-DuhemequationsderivedinthelettercanservetojustifyanappropriateformfortheLa-grangeparameterscontrollingthermalequilibrium,withoutneedofanychangeofvariables.ThisleadstoaframeworkforTsallisThermodynamicswhichisfreefromrecentcriticismsraisedbyNauenberg[Phys.Rev.E67,036114(2003)cond-mat/0210561]andGross[Physica(Amsterdam)305,99(2002)cond-mat/0106496].ThisisaccomplishedthroughadirectconnectionwithHill’s82Nanothermodynamics.
]PACSnumbers:05.70.Ln,05.20.Gg,05.40.-a
chemInarecentletter[1]VivesandPlanes(VP)discussTsallisThermodynamics(TT)derivingageneralization-toftheGibbs-Duhem(GD)equationwhichreducestotheattraditionalonewhentheentropicparameterqtendstosunity.Theauthorssuggestachangeofvariablesthat.taallowstorecoverstandardThermodynamics,proposingmexpressionsfortheLagrangeparameters(LPs)whichare-supposedtobethosecontrollingmutualequilibriumbe-dtweenthermodynamicsystems.AlthoughtheapproachnleadingtoEq.(9)in[1]iscorrectandinsightful,theochangeofvariablesandsubsequentanalysisisunnec-c[essaryandleadstocontroversialanalyticalexpressions fortheLPsthathavebeenthekernelofthemaincrit-1vicismsraisedagainstTT[2].Wepointoutherethat2Eqs.(4),(8)and(9)in[1]canserveasabasistojus-4tifythattheLPsyαin[1]arethephysicallymeaningful6onescontrarilytowhatissuggestedbytheauthorsand0otherpractitionersinthe eld(seeRefs.[12]and[13]1in[1]).Thisleadsustoestablishequilibriumproperties30forTTovercomingpreviousdi culties[2].Theyαcan/beviewedastheLPscontrolling(nano)thermodynamictaequilibriumand,contrarilytowhatisclaimedbythemauthors,thesearethenintensivevariables.Toproceed-furtherletusintroduceHill’sformalismofNanothermo-ddynamics(NT)[3,4].Hill’sNTisarigorousextensionnofstandardthermodynamicstosystemsthatexperiencecoequilibrium uctuationsofarbitrarystrenght(“smallsys-:vtems”)inwhichallquantitiesinvolvedhaveaclearphys-iicalmeaning.WeprovidenextaconnectionbetweenTTXandNT.Itisinterestingtonotethatthe(entropic)EulerrandGDequationsinNT(seeEqs.(1-72)and(1-75)inaRef.[4])are,respectively
(rewrittenhereinVPnotation)
yα,H Xα H=S J(1)
α
Xα Hdyα,H=dJ
(2)
α
SubindexHmeans“Hill’svariables”whicharethephys-ical(averaged)extensive( Xα )andintensive(yα)ones.
SisthephysicalentropyforonesystemandJisthe
subdivision(entropic)potential.Jisanintensivevari-ableandthenumberofsystemsλisitsconjugateexten-siveone(inourcase,asin[1],wearedealingwithonly
onesystemandλ=1isimplicitlyconsideredintheseequations).Bydi erentiatingEq.(1)andusingEq.(2)itcanbeseenthattheentropyfor onesystemSsatis esthedi erentialequationdS=αyα,Hd Xα formallyidenticaltoEq.(4)in[1].ItisclearHwhichisthatthestructureofVPequationsandthoseofHillisthesameandtheformercanbeobtainedfromthelatterifS≡S ,yα,H≡yα, Xα H≡ Xα qandthefollowingcorrespon-denceismade
J≡S
[1+(1 q)S
]
ln[1+(1 q)S ]
1 q[1+(1 qA
A)SA ]ln[1+(1 qA)SA
]
=SB
1
nonextensive statistical mechanics theory proposed by Tsallis,closely associated ...Stanley H E. Stochastic process with ultraslow convergence to a gaussian: ...
Extensive Game with Impe... 暂无评价 27页 ...[1] and, for critical comments, from Shalizi [...Tsallis Statistics, Statistical Mechanics for Non-...
Consider a set E of mutually exclusive events Ei...associated with the non extensiveness of the ... Havrda-Charvat entropy(HC)[9] and Tsallis ...
Extensive Game with Impe... 暂无评价 27页 ...[1] and, for critical comments, from Shalizi [...Tsallis Statistics, Statistical Mechanics for Non-...
我要评论