On the origin of escort distributions for q-entropies

TL;DR

This paper explores the origin of escort distributions in q-entropy within non-additive thermodynamics, linking them to the geometric limit of manifolds with warped product metrics and interpreting the parameter q as a dimension related to phase space structure.

Contribution

It provides a geometric interpretation of escort distributions and the entropic parameter q in terms of Gromov-Hausdorff limits and fibration structures of phase spaces.

Findings

Escort distributions originate from geometric limits of manifolds.

The entropic parameter q is interpreted as a dimension.

Provides a new geometric perspective on q-entropy.

Abstract

We present an argument about the origin of escort distributions used in conjunction with the q-entropy in non-additive thermo-statistics. The origin of the escort distributions is ascribed to the fact that the effective statistical description of the underlying system is provided by the measured Gromov-Hausdorff limit of a sequence of manifolds having a warped product metric structure. We interpret the entropic parameter \ q \ appearing in escort distributions as a "dimension" related to the fibration structure of the underlying phase spaces.