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

T. Wada
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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.

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T. Wada. 2002-08-10. Model-free derivations of the Tsallis factor: constant heat capacity derivation. https://doi.org/10.1016/j.physleta.2003.09.056

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