Heat and entropy in nonextensive thermodynamics: transmutation from Tsallis theory to Rényi-entropy-based theory

Macroscopic nonextensive thermodynamics is studied without recourse to microscopic statistical mechanics. Taking the Tsallis entropy as an example, it is shown that the concept of the physical temperature introduced through the generalized zeroth law of thermodynamics necessarily leads to modification of Clausius’ definition of the thermodynamic entropy. It is also shown, by applying this generalized Clausius entropy to a composite nonextensive system, how the entropy and the quantity of heat behave in an arbitrary thermodynamic process. The results presented here indicate that, even starting with a nonextensive entropy, the thermodynamic entropy appearing at the macroscopic level has to be extensive, in accordance with Carathéodoryʹs theorem. This fact can be observed as transmutation from nonextensive Tsallis theory to extensive Rényi-entropy-based theory.