Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature

TL;DR

This paper explores the theoretical relationship between the Fisher temperature T_F and the ordinary temperature T, establishing reciprocity relations and interpreting T_F within the canonical ensemble framework.

Contribution

It demonstrates the existence of reciprocity relations between T_F and T, providing a new interpretation of T_F in statistical mechanics.

Findings

Reciprocity relations between T_F and T are established.

A new interpretation of Fisher temperature T_F in the canonical ensemble is proposed.

Theoretical framework connecting Fisher information and thermodynamic temperature is developed.

Abstract

Frieden and Soffer conjectured some years ago the existence of a ``Fisher temperature" T_F that would play, with regards to Fisher's information measure I, the same role that the ordinary temperature T plays vis-a-vis Shannon's logarithmic measure. Here we exhibit the existence of reciprocity relations between T_F and T and provide an interpretation with reference to the meaning of T_F for the canonical ensemble.