Legendre structure of the thermostatistics theory based on the Sharma-Taneja-Mittal entropy

TL;DR

This paper explores the Legendre structure of thermostatistics based on the Sharma-Taneja-Mittal entropy, a two-parameter family of entropies that produce power-law distributions suitable for complex systems.

Contribution

It introduces a generalized thermodynamics framework using STM entropy, analyzing thermodynamical potentials and their properties, and specializes results to one-parameter cases.

Findings

Established the Legendre structure for STM-based thermostatistics

Derived relationships between thermodynamical potentials and entropy

Analyzed properties of one-parameter entropy specializations

Abstract

The statistical proprieties of complex systems can differ deeply for those of classical systems governed by Boltzmann-Gibbs entropy. In particular, the probability distribution function observed in several complex systems shows a power law behavior in the tail which disagrees with the standard exponential behavior showed by Gibbs distribution. Recently, a two-parameter deformed family of entropies, previously introduced by Sharma, Taneja and Mittal (STM), has been reconsidered in the statistical mechanics framework. Any entropy belonging to this family admits a probability distribution function with an asymptotic power law behavior. In the present work we investigate the Legendre structure of the thermostatistics theory based on this family of entropies. We introduce some generalized thermodynamical potentials, study their relationships with the entropy and discuss their main proprieties. Specialization of the results to some one-parameter entropies belonging to the STM family are presented.