MaxEnt, second variation, and generalized statistics

TL;DR

This paper investigates the conditions under which Tsallis-entropy distributions maximize for different types of Hamiltonians, using functional analysis to distinguish between heavy tail and compact support cases.

Contribution

It demonstrates that only heavy tail Tsallis distributions guarantee a maximum for lower bound Hamiltonians, providing a functional analysis approach to this problem.

Findings

Heavy tail distributions guarantee maxima for Tsallis-entropy with lower bound Hamiltonians.

Compact support distributions require case-by-case analysis to determine maxima.

Functional analysis tools are effective in studying Tsallis-entropy maximization.

Abstract

There are two kinds of Tsallis-probability distributions: heavy tail ones and compact support distributions. We show here, appealing to functional analysis' tools, that for lower bound Hamiltonians only the first type guarantees a maximum for Tsallis-entropy. In the compact support instance, a case by case analysis is necessary in order to tackle the issue.