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, β. Similarly, the physical pressure is also to be defined in accordance with this law. These facts lead to modifications of the first law of thermodynamics as well as some of thermodynamic relations for nonextensive systems. Here, taking the generalized 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 modified. It is shown that the definition of specific heat remains form invariant. Thus, the thermodynamic relations proposed by Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are rectified. As an application, the classical gas model is reexamined and, in marked contrast with the previous result using the unphysical temperature and pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics. PACS: 05.70.-a; 05.20.-y; 05.90.+m 1