  Stochastic Spatio-Temporal processes are prevalent across domains ranging
from modeling of plasma to the turbulence in fluids to the wave function of
quantum systems. This letter studies a measure-theoretic description of such
systems by describing them as evolutionary processes on Hilbert spaces, and in
doing so, derives a framework for spatio-temporal manipulation from fundamental
thermodynamic principles. This approach yields a variational optimization
framework for controlling stochastic fields. The resulting scheme is applicable
to a wide class of spatio-temporal processes and can be used for optimizing
parameterized control policies. Our simulated experiments explore the
application of two forms of this approach on four stochastic spatio-temporal
processes, with results that suggest new perspectives and directions for
studying stochastic control problems for spatio-temporal systems.
