Density operators that extremize Tsallis entropy and thermal stability effects

TL;DR

This paper derives analytical forms of discrete probability distributions that maximize Tsallis entropy under fixed variance, revealing how non-extensivity influences system stability and physical plausibility.

Contribution

It provides a general analytical framework for density operators extremizing Tsallis entropy, illustrating the impact of non-extensivity on thermal stability.

Findings

Varying the non-extensivity index q affects system stability.

Distributions can become unphysical with infinite energy at certain q values.

The approach applies to systems with discrete Hamiltonian eigenstates.

Abstract

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PD's as "weights" leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis' non-extensivity index $q$ one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy.