  Motivated by the recent shocking results from RHIC and LHC that show
quark-gluon plasma signatures in small systems, we study a simple model of a
massless, noninteracting scalar field confined with Dirichlet boundary
conditions. We use this system to investigate the finite size corrections to
thermal field theoretically derived quantities compared to the usual
Stefan-Boltzmann limit of an ideal gas not confined in any direction. Two
equivalent expressions with different numerical convergence properties are
found for the free energy in $D$ rectilinear spacetime dimensions with $c\le
D-1$ spatial dimensions of finite extent. We find that the First Law of
Thermodynamics generalizes such that the pressure depends on direction but that
the Third Law is respected. For systems with finite dimension(s) but infinite
volumes, such as a field constrained between two parallel plates or a
rectangular tube, the relative fluctuations in energy are zero, and hence the
canonical and microcanonical ensembles are equivalent. We present precise
numerical results for the free energy, total internal energy, pressure,
entropy, and heat capacity of our field between parallel plates, in a tube, and
in finite volume boxes of various sizes in 4 spacetime dimensions. For
temperatures and system sizes relevant for heavy ion phenomenology, we find
large deviations from the Stefan-Boltzmann limit for these quantities,
especially for the pressure. Further investigation of an isolated system of
fields constrained between parallel plates reveals a divergent isoenergetic
compressibility at a critical length $L_c\sim1/T$. We have thus discovered a
new second order phase transition via a first principles calculation, a
transition that is driven by the size of the system.
