Statistical Mechanics of Unconfined Systems: Challenges and Lessons

TL;DR

This paper provides an exact maximum entropy solution for unconfined ideal gases in anti-de Sitter space, introducing a new method to identify dynamical constraints from local measurements without prior global information.

Contribution

It develops a novel approach to determine stationary distributions in unconfined systems, expanding the applicability of statistical mechanics to broader contexts.

Findings

Derived necessary conditions for normalizable stationary distributions.

Introduced a new method for identifying dynamical constraints from local data.

Provided an exact solution for an unconfined ideal gas in anti-de Sitter space.

Abstract

Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an unconfined ideal gas in an anti-de Sitter background. Notwithstanding the gas's freedom to move in an infinite volume, we establish necessary conditions for the stationary probability distribution to be normalizable. As a part of our analysis, we develop a novel method for identifying dynamical constraints based on local measurements. With no appeal to \emph{a priori} information about globally-defined conserved quantities, it is thereby applicable to a much wider range of problems.