Thermal measurements of stationary nonequilibrium systems: A test for generalized thermostatistics

TL;DR

This paper investigates the behavior of a gas thermometer in contact with a nonequilibrium classical system, showing it evolves towards Levy distributions and questioning the applicability of Tsallis's nonextensive thermostatistics.

Contribution

It introduces a kinetic framework demonstrating Levy distributions emerge in nonequilibrium systems and critiques the relevance of Tsallis distributions for describing system-thermometer equilibrium.

Findings

Thermometer reaches Levy velocity distribution in stationary nonequilibrium.

Tsallis's nonextensive distributions are not suitable for the thermometer's stationary state.

Highlights the need for a generalized thermostatistical theory unifying Levy and Maxwell distributions.

Abstract

We show that a gas thermometer in contact with a stationary classical system out of thermal (Boltzmann) equilibrium evolves, under very general conditions, towards a state characterized by a Levy velocity distribution. Our approach is based on a kinetic-like equation that applies to a wide class of models for the system-thermometer interaction. The results clarify the role of non-exponential energy distributions as possible generalizations of the Boltzmann distribution for systems where the usual formulation of thermostatistics may not apply. In particular, they show that the power-law distributions derived from Tsallis's nonextensive formalism are irrelevant to the stationary state of the thermometer, thus failing to give a consistent description of the system-thermometer equilibrium. We point out the need of a generalized thermostatistical formulation able to give a unified frame to Levy and Maxwell distributions.