Parameter estimation in nonextensive thermostatistics

TL;DR

This paper applies statistical estimation theory to equilibrium statistical physics, extending identities to generalized exponential families involving escort distributions, with a percolation model example.

Contribution

It demonstrates that identities from exponential family models extend to generalized families with escort distributions, enriching the theoretical framework.

Findings

Identities involving derivatives of the partition sum are valid for generalized exponential families.

A specific identity relating cluster properties in a percolation model is derived.

The approach links statistical estimation concepts with nonextensive thermostatistics.

Abstract

Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the existence of identities, obtained by taking derivatives of the logarithm of the partition sum. It is shown that these identities still exist for models belonging to generalised exponential families, in which case they involve escort probability distributions. The percolation model serves as an example. A previously known identity is derived. It relates the average number of sites belonging to the finite cluster at the origin, the average number of perimeter sites, and the derivative of the order parameter.