Quasicanonical Gibbs distribution and Tsallis nonextensive statistics

TL;DR

This paper derives a quasicanonical Gibbs distribution for finite thermostats, establishing a connection to Tsallis nonextensive statistics and explaining recent temperature fluctuation models through statistical and kinetic analysis.

Contribution

It introduces a quasicanonical Gibbs distribution framework that links finite thermostat effects to Tsallis statistics, providing a theoretical basis for temperature fluctuations.

Findings

Tsallis parameter q relates to the number of particles in the quasithermostat.

The chi-square distribution of temperature fluctuations can be explained via particle momenta.

Time scale hierarchy influences the emergence of Tsallis distribution in systems.

Abstract

We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and thermodynamics, with Tsallis parameter q is found to be related to the number of particles in the quasithermostat. We show that the chi-square distribution of fluctuating temperature used recently by Beck can be partially understood in terms of normal random momenta of particles in the quasithermostat. Also, we discuss on the importance of the time scale hierarchy and fluctuating probability distribution functions in understanding of Tsallis distribution, within the framework of kinetics of dilute gas and weakly inhomogeneous systems.