Information measures based on Tsallis' entropy and geometric considerations for thermodynamic systems

TL;DR

This paper explores the thermodynamic behavior of quantum systems using a geometric approach based on Tsallis' entropy and q-divergence, providing generalized operator expressions and a fundamental tensor.

Contribution

It introduces a geometric analysis framework for nonextensive thermodynamics using Tsallis' entropy and q-divergence, extending operator variance and covariance concepts.

Findings

Developed a geometric framework for quantum thermodynamics

Derived generalized operator variance and covariance expressions

Analyzed the structure of the state space in nonextensive systems

Abstract

An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks, making use of the q-divergence derived from Tsallis' entropy. Generalized expressions for operator variance and covariance are considered, in terms of which the fundamental tensor is given.