On the thermodynamic stability conditions of Tsallis' entropy

The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw (Phys. Lett. A 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...

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Bibliographic Details
Published inPhysics letters. A Vol. 297; no. 5; pp. 334 - 337
Main Author Wada, Tatsuaki
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.05.2002
Subjects
Pseudo-additivity
Thermodynamic stability
Tsallis' entropy
Thermodynamic stability
Pseudo-additivity
Tsallis' entropy
05.20.-y
05.90.+m
05.70.-a
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Summary:The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw (Phys. Lett. A 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 nonadditivity of Tsallis' entropy. Taking account of the nonadditivity 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 Rényi entropies.
ISSN:0375-9601
1873-2429
DOI:10.1016/S0375-9601(02)00378-X