Macroscopic thermodynamics based on composable nonextensive entropies

Composability of entropy implies that entropy of the total system composed of independent subsystems is given by a function of entropies of the subsystems. It is shown that the zeroth law of thermodynamics naturally leads to Tsallis-type pseudoadditivity of the composable entropies. Then, macroscopic thermodynamics is discussed based on the simplest example of such entropies. It is found that, even if nonextensive entropy is initially employed, the resulting thermodynamic entropy is necessarily extensive at the macroscopic level, in accordance with Caratheodory's theorem. This result depends crucially on the assumptions that the subsystems are independent and the total energy is the SLIM of the energies of the subsystems. (C) 2002 Elsevier Science B.V. All rights reserved.