  We consider dynamical systems evolving near an equilibrium statistical state
where the interest is in modelling long term behavior that is consistent with
thermodynamic constraints. We adjust the distribution using an
entropy-optimizing formulation that can be computed on-the- fly, making
possible partial corrections using incomplete information, for example measured
data or data computed from a different model (or the same model at a different
scale). We employ a thermostatting technique to sample the target distribution
with the aim of capturing relavant statistical features while introducing mild
dynamical perturbation (thermostats). The method is tested for a point vortex
fluid model on the sphere, and we demonstrate both convergence of equilibrium
quantities and the ability of the formulation to balance stationary and
transient- regime errors.
