  We define a natural coarse-graining procedure which can be applied to any
closed equilibrium quantum system described by a density matrix ensemble and we
show how the coarse-graining leads to the Gaussian and canonical ensembles.
After this motivation, we present two ways of evaluating the Gaussian
expectation values with lattice simulations. The first one is computationally
demanding but general, whereas the second employs only canonical expectation
values but it is applicable only for systems which are almost thermodynamical.
