Troublesome aspects of the Renyi-MaxEnt treatment

TL;DR

This paper investigates the feasibility of a Renyi-based thermodynamics, revealing a hidden relation in the variational problem that leads to anomalous thermodynamic results, ultimately showing such a thermodynamics does not exist.

Contribution

It uncovers a hidden relation in the Renyi-MaxEnt variational problem and demonstrates the non-existence of a consistent Renyi-associated thermodynamics.

Findings

No consistent Renyi thermodynamics exists.

A hidden relation links Lagrange multipliers with mean energy and Renyi parameter.

Renyi-MaxEnt approach yields anomalous thermodynamic results.

Abstract

We study in great detail the possible existence of a Renyi-associated thermodynamics, with negative results. In particular, we uncover a hidden relation in the Renyi's variational problem (MaxEnt). This relation connects the two associated Lagrange multipliers (Canonical Ensemble) with the mean energy $<U>$ and the Renyi parameter $\alpha$. As a consequence of such relation, we obtain anomalous Renyi-MaxEnt thermodynamic results.