The Boltzmann temperature and Lagrange multiplier

TL;DR

This paper explores the relationship between Boltzmann temperature and Lagrange multipliers in nonextensive thermostatistics, clarifying the nature of the physical temperature in Tsallis' framework and its dependence on energy.

Contribution

It demonstrates that the physical temperature in Tsallis' ensemble is the ensemble average of the Boltzmann temperature, clarifying their relationship.

Findings

The Boltzmann temperature depends on energy unless q=1.

The physical temperature is the ensemble average of the Boltzmann temperature.

The paper clarifies the role of Lagrange multipliers in nonextensive thermodynamics.

Abstract

We consider the relation between the Boltzmann temperature and the Lagrange multipliers associated with energy average in the nonextensive thermostatistics. In Tsallis' canonical ensemble, the Boltzmann temperature depends on energy through the probability distribution unless $q=1$. It is shown that the so-called 'physical temperature' introduced in [Phys. Lett. A \textbf{281} (2001) 126] is nothing but the ensemble average of the Boltzmann temperature.