A note on non-thermodynamical applications of non-extensive statistics

TL;DR

This paper discusses the limitations of applying non-extensive statistical mechanics, specifically Tsallis's formalism, to non-thermodynamical processes, highlighting issues with defining constraints and the non-uniqueness of the non-extensivity index q.

Contribution

It critically examines the applicability of Tsallis's non-extensive statistics outside thermodynamics, emphasizing the ambiguity in defining constraints and the non-uniqueness of the q parameter.

Findings

Constraints in non-thermodynamical processes are not well-defined.

Any probability distribution can be derived using Jaynes's principle with suitable constraints.

No unambiguous non-extensivity index q can be assigned to non-thermodynamical processes.

Abstract

It is pointed out that the constraint to be imposed to the maximization of the entropy for processes outside the class of thermodynamical systems, is generally not well defined. In fact, any probability distribution can be derived from Jaynes's principle with a suitable choice of the constraint. In the case of Tsallis's non-extensive formalism, this implies that it is not possible to establish any connection between specific non-thermodynamical processes and non-extensive mechanisms and, in particular, to assign any unambiguous non-extensivity index q to those processes.