Non-extensive statistical mechanics: Gibbs-type formula, existence and uniqueness of its solution

TL;DR

This paper rigorously proves the existence and uniqueness of solutions for the Gibbs-type formula in non-extensive statistical mechanics and introduces a new extremal problem to simplify deriving the formula.

Contribution

It provides rigorous mathematical results on solution existence and uniqueness and proposes a novel extremal problem approach for deriving the Gibbs-type formula.

Findings

Proved existence and uniqueness of solutions for the Gibbs-type formula.

Introduced a new conditional extremal problem for simplified derivation.

Enhanced understanding of non-extensive statistical mechanics solutions.

Abstract

Existence and uniqueness results for the solution of the Gibbs-type formula from non-extensive mechanics are derived rigorously. A new conditional extremal problem is proposed to get in a more simple way the Gibbs-type formula itself.