  We analyze the effect of a finite volume on the thermodynamic potentials of a
relativistic quantum field theory defined on a hypertorus at vanishing chemical
potential. Using the symmetries of the Euclidean partition function, we
interpret the thermodynamic observables as the expectation value of the
energy-momentum tensor in the same theory living on a $\beta\times L^2$ volume.
In the case where the screening correlation lengths in the thermal system are
finite, we obtain a closed formula for the leading finite volume effects in
terms of the smallest screening mass. This formula can be used to estimate, and
possibly correct for, the leading finite volume effects in lattice calculations
of QCD thermodynamics.
