Eur. Phys. J. B 30, 543-549 (2002)
https://doi.org/10.1140/epjb/e2002-00412-6

Generalized thermostatistics based on the Sharma-Mittal entropy and escort mean values

¹ Institute for Theoretical Physics, University of Münster Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
² Faculty of Astronomy and Geophysics, National University La Plata, C.C. 727, 1900 La Plata, Argentina

Corresponding author: ^a tdfrank@uni-muenster.de

Received: 27 June 2002
Published online: 31 December 2002

Abstract

A generalized thermostatistics is developed for an entropy measure introduced by Sharma and Mittal. A maximum-entropy scheme involving the maximization of the Sharma and Mittal entropy under appropriate constraints expressed as escort mean values is advanced. Maximum-entropy distributions exhibiting a power law behavior in the asymptotic limit are obtained. Thus, results previously derived for the Renyi entropy and the Tsallis entropy are generalized. In addition, it is shown that for almost deterministic systems among all possible composable entropies with kernels that are described by power laws the Sharma-Mittal entropy is the only entropy measure that gives rise to a thermostatistics based on escort mean values and admitting of a partition function.