  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.
