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

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

2002-08-10

arxiv.org/abs/cond-mat/0208205v1

Physics

Condensed Matter

Statistical Mechanics

11 pages, no figure, elsert

Scientific paper

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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