Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical te mperature in nonextensive statistical mechanics is different from the inver se of the Lagrange multiplier, beta. This fact leads to modifications of so me of thermodynamic relations for nonextensive systems. Here, taking the fi rst law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius' definition of the thermodynamic entro py has to be appropriately changed, and accordingly the thermodynamic relat ions proposed by Tsallis et al. (Physica A 261 (1998) 534) are also to be m odified. 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 unphy sical temperature and the unphysical pressure, the specific heat and the eq uation of state are found to be similar to those in ordinary extensive ther modynamics. (C) 2001 Elsevier Science B.V. All rights reserved.