On the thermodynamic stability conditions of Tsallis' entropy

Details On the thermodynamic stability conditions of Tsallis' entropy On the thermodynamic stability conditions of Tsallis' entropy

2002-01-21

arxiv.org/abs/cond-mat/0201368v2

Phys. Lett. A 297 (2002) 334-337

Physics

Condensed Matter

Statistical Mechanics

Corrected some errors and typos. 7 pages, LaTeX2e, elsart, submitted to Phys. Lett. A

Scientific paper

10.1016/S0375-9601(02)00378-X

The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw [Phys. Lett. A {\bf 198} (1995) 119] has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient to guarantee thermodynamic stability for all values of $q$ due to the non-additivity of Tsallis' entropy. Taking account of the non-additivity the differential form of the TSC for Tsallis entropy is explicitly derived. It is shown that the resultant TSC for Tsallis' entropy is equivalent to the positivity of the standard specific heat. These results are consistent with the relation between Tsallis and R\'enyi entropies.

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