Statistical Mechanics of Unconfined Systems: Challenges and Lessons

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.