Temperature definition and fundamental thermodynamic relations in incomplete statistics (Q813677)

Nonextensive statistical mechanics has been developed by many researchers. The incomplete statistics (IS) proposed by Wang in 2001 is based on Tsallis entropy and a different normalization rule, involving the q'th powers of the probabilities. However, in the IS framework, several basic questions are still open to investigation. One of these questions is the relation between the physical temperature and the Lagrange multplier in the derivation of the probability function. Other questions are the fundamental thermodynamic relations in IS, or the role of the zeroth law of thermodynamics in nonextensive statistical mechanics. In this paper a temperature defintion and a set of thermodynamic relations are derived, based on the basic assumptions and results of nonadditive IS. Temperature is shown to be proportional to the inverse of a modified Lagrange multiplier. The thermodynamic relations all involve the parameter q of the normalization, but can be brought into a form similiar to the classical thermodynamic relations.