  A gas in a box is perhaps the most important model system studied in
thermodynamics and statistical mechanics. Usually, studies focus on the gas,
whereas the box merely serves as an idealized confinement. The present article
focuses on the box as the central object and develops a thermodynamic theory by
treating the geometric degrees of freedom of the box as the degrees of freedom
of a thermodynamic system. Applying standard mathematical methods to the
thermodynamics of an empty box allows equations with the same structure as
those of cosmology and classical and quantum mechanics to be derived. The
simple model system of an empty box is shown to have interesting connections to
classical mechanics, special relativity, and quantum field theory.
