Temperature and pressure in nonextensive thermostatistics.pdfVIP

a r X i v : p h y s i c s / 0 3 1 1 0 3 4 v 1 [ p h y s i c s .d a t a - a n ] 7 N o v 2 0 0 3 Temperature and pressure in nonextensive thermostatistics Q.A. Wang, L. Nivanen, A. Le Me?haute?, Institut Supe?rieur des Mate?riaux et Me?caniques Avance?s, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France and M. Pezeril Laboratoire de Physique de l’e?tat Condense?, Universite? du Maine, 72000 Le Mans, France Abstract The definitions of the temperature in the nonextensive statistical thermodynamics based on Tsallis entropy are analyzed. A definition of pressure is proposed for nonadditive systems by using a nonadditive effective volume. The thermodynamics of nonadditive photon gas is discussed on this basis. We show that the Stefan-Boltzmann law can be preserved within nonextensive thermodynamics. PACS : 05.20.-y, 05.70.-a, 02.50.-r 1 Introduction The nonextensive statistical mechanics (NSM)[1] based on Tsallis entropy is believed by many to be a candidate replacing Boltzmann-Gibbs statistics (BGS) for nonextensive or nonadditive systems which may show probability distributions different from that of BGS. So according the common belief, NSM, just as BGS, should be able to address thermodynamic functions and intensive variables like temperature T , pressure P , chemical potential μ etc. Although the Legendre transformation between the thermodynamic functions is preserved in some versions of NSM with sometimes certain deformation, the definition of intensive variables is not obvious if the thermodynamic functions 1 such as entropy S, energy U or free energy F are nonadditive. There are sometimes misleading calculations using β = 1/T = ( ?S ?U ) V (let Boltzmann constant k = 1) and P = ? ( ?F ?V ) T or P = 1 3 U V (for photon gas) without specifying the nonadditivity (or additivity) of each functions or noticing that additive internal energy U and volume V associated with nonadditive S and F will lead to non-intensive temperature or pressure which would make the ther