H-theorems for the Tsallis and Renyi entropies

Mariz [Phys. Lett. A 165 (1992) 409] recently analyzed the time evolution of the Tsallis entropy SqT and the Renyi entropy SqR based on the master equation and the assumption of detailed balance. Mariz restricted attention to situations where the equilibrium probability distribution is uniform, for...

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Bibliographic Details
Published in:Physics letters. A 1993-04, Vol.175 (3-4), p.169-170
Main Author: Ramshaw, John D.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Thermodynamics
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Summary:Mariz [Phys. Lett. A 165 (1992) 409] recently analyzed the time evolution of the Tsallis entropy SqT and the Renyi entropy SqR based on the master equation and the assumption of detailed balance. Mariz restricted attention to situations where the equilibrium probability distribution is uniform, for which he showed that dSqTdt and dSqRdt have the same sign as the parameter q. Here we show that these results continue to hold in the absence of detailed balance. We also present the generalization to cases with nonuniform equilibrium distributions, for which it is necessary to appropriately redefine the entropy relative to equilibrium.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(93)90820-P