Model-free derivations of the Tsallis factor: constant heat capacity derivation

摘要

The constant temperature derivation, which is a model-free derivation of theBoltzmann factor, is generalized in order to develop a new simple model-freederivation of a power-law Tsallis factor based on an environment with constantheat capacity. It is shown that the integral constant T_0 appeared in the newderivation is identified with the generalized temperature T_q in Tsallisthermostatistics. A constant heat capacity environment is proposed as aone-real-parameter extension of the Boltzmann reservoir, which is a modelconstant temperature environment developed by J.J. Prentis et al. [Am. J. Phys.67 (1999) 508] in order to naturally obtain the Boltzmann factor. It is alsoshown that the Boltzmann entropy of such a constant heat capacity environmentis consistent with Clausius' entropy.