Equilibrium Distributions in Open and Closed Statistical Systems

TL;DR

This paper derives Boltzmann-Gibbs and Maxwellian distributions geometrically, demonstrating their universality in both open and closed homogeneous systems in the thermodynamic limit.

Contribution

It provides a geometric derivation of fundamental equilibrium distributions, highlighting their independence from system openness or closure.

Findings

Distributions derived from phase space geometry under equiprobability.

Equilibrium distributions are identical for open and closed systems in the thermodynamic limit.

Geometric approach offers a unified view of statistical mechanics distributions.

Abstract

In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by working out the properties of the volume or the surface of the respective geometries delimited in phase space by an additive constraint. That is, the asymptotic equilibrium distributions in the thermodynamic limit are independent of considering open or closed homogeneous statistical systems.