Equivalence of two thermostatistical formalisms based on the Havrda&Charvat-Daroczy-Tsallis entropies

Details Equivalence of two thermostatistical formalisms based on the Havrda&Charvat-Daroczy-Tsallis entropies Equivalence of two thermostatistical formalisms based on the Havrda&Charvat-Daroczy-Tsallis entropies

1999-08-13

arxiv.org/abs/cond-mat/9908207v4

Physics

Condensed Matter

Statistical Mechanics

4 pages, no figures

Scientific paper

We show that the latest thermostatistical formalism based on the Havrda & Charvat-Dar\'oczy-Tsallis entropy $S_q [ \rho ] = (q-1)^{-1}(1- tr (\rho^q))$ proposed by Tsallis, Mendes and Plastino is {\em equivalent} to the first one proposed by Tsallis in 1988. Here, equivalent means: {\em the ``equilibrium'' state predicted by either formalism using $q$ leads to the same expectation values for all observables as that predicted by the other formalism using $1/q$''}. We also point out once again that the basic property of {\em transitivity of equilibrium} (e.g., the $0^{th}$ Law of Thermodynamics) fails in these formalisms.

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