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

TL;DR

This paper generalizes the model-free derivation of the Boltzmann factor to derive a power-law Tsallis factor using an environment with constant heat capacity, linking it to Tsallis thermostatistics.

Contribution

It introduces a new simple model-free derivation of the Tsallis factor based on constant heat capacity environments, extending the Boltzmann reservoir concept.

Findings

Derivation of the Tsallis factor from a constant heat capacity environment.

Identification of the integral constant T_0 with the generalized temperature T_q.

Consistency of the entropy with Clausius' entropy.

Abstract

The constant temperature derivation, which is a model-free derivation of the Boltzmann factor, is generalized in order to develop a new simple model-free derivation of a power-law Tsallis factor based on an environment with constant heat capacity. It is shown that the integral constant T_0 appeared in the new derivation is identified with the generalized temperature T_q in Tsallis thermostatistics. A constant heat capacity environment is proposed as a one-real-parameter extension of the Boltzmann reservoir, which is a model constant 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 also shown that the Boltzmann entropy of such a constant heat capacity environment is consistent with Clausius' entropy.