Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This fact leads to modifications of some of thermodynamic relations for nonextensive systems. Here, taking the first law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius' definition of the thermodynamic entropy has to be appropriately changed, and accordingly the thermodynamic relations proposed by Tsallis et al. (Physica A 261 (1998) 534) are also to be modified. It is shown that the definition of specific heat and the equation of state remain form invariant. As an application, the classical gas model is reexamined and, in marked contrast with the previous result obtained by Abe (Phys. Lett, A 263 (1999) 424; Erratum: 267 (2000) 456) using the unphysical temperature and the unphysical pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics. (C) 2001 Elsevier Science B.V. All rights reserved.