Reconciliation between the Tsallis maximum entropy principle and large deviation theory

TL;DR

This paper derives necessary conditions that reconcile the q-maximum entropy principle with large deviation theory, ensuring consistency between generalized statistical mechanics and probabilistic large deviation properties.

Contribution

It introduces new necessary conditions that unify the Tsallis maximum entropy principle with large deviation theory, addressing previous limitations and providing practical numerical examples.

Findings

Necessary conditions established for the reconciliation

Conditions avoid prohibitive constraints of previous methods

Numerical examples demonstrate the applicability

Abstract

The necessary conditions (NC) that reconcile canonical probability distributions obtained from the q-maximum entropy principle, subjected to both i) the additive duality of generalized statistics and ii) normal averages expectations with the large deviation theory, are derived. The validity of these necessary conditions is established on the basis of a result concerning large deviation properties of conditional measures. The NC for normal averages expectations are advantageous because they avoid the excessively prohibitive conditions obtained by previous studies when employing other forms for defining q-expectations. Numerical examples for an exemplary case are provided.