Generalized molecular chaos hypothesis and H-theorem: Problem of constraints and amendment of nonextensive statistical mechanics

TL;DR

This paper clarifies the correct averaging method in nonextensive statistical mechanics, demonstrating that the normal average aligns with the molecular chaos hypothesis and H-theorem, leading to an amended formulation of the theory.

Contribution

It identifies the normal average as the correct mean in nonextensive statistical mechanics, challenging the prevalent use of the q-average and revising the theoretical framework accordingly.

Findings

Normal average is consistent with the generalized Stosszahlansatz and H-theorem.

The q-average is shown to be incompatible with the molecular chaos hypothesis.

The formulation of nonextensive statistical mechanics is amended based on the normal average.

Abstract

Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated H-theorem, whereas the q-average widely used in the relevant literature is not. In the course of the analysis, the distributions with finite cut-off factors are rigorously treated. Accordingly, the formulation of nonextensive statistical mechanics is amended based on the normal average. In addition, the Shore-Johnson theorem, which supports the use of the q-average, is carefully reexamined, and it is found that one of the axioms may not be appropriate for systems to be treated within the framework of nonextensive statistical mechanics.