Physical temperature and the meaning of the q parameter in Tsallis statistics

TL;DR

This paper explores the relationship between physical temperature, the Tsallis q parameter, and the density of states in systems with constant heat capacity, using the Ising model as an example.

Contribution

It clarifies the distinction between the measurable temperature and the function beta(E) derived from the density of states, linking these to the Tsallis q parameter.

Findings

beta(E) differs from the physical temperature

Connections established between beta(E), temperature, and q

Illustration using the one-dimensional Ising model

Abstract

We show that the function beta(E) derived from the density of states of a constant heat capacity reservoir coupled to some system of interest is not identical to the physically measurable (transitive) temperature. There are, however, connections between the two quantities as well as with the Tsallis parameter q. We exemplify these connections using the one-dimensional Ising model in the "dynamical ensemble".