  While techniques to compute thermal fluctuation induced, or pseudo-Casimir,
forces in equilibrium systems are well established, the same is not true for
non-equilibrium cases. We present a general formalism that allows us to
unambiguously compute non-equilibrium fluctuation induced forces by specifying
the energy of interaction of the fluctuating fields with the boundaries. For a
general class of classical fields with dissipative dynamics, we derive a very
general relation between the Laplace transform of the time-dependent force and
the static partition function for a related problem with a different
Hamiltonian. In particular, we demonstrate the power of our approach by
computing, for the first time, the explicit time dependence of the
non-equilibrium pseudo-Casimir force induced between two parallel plates, upon
a sudden change in the temperature of the system. We also show how our results
can be used to determine the steady-state behavior of the non-equilibrium force
in systems where the fluctuations are driven by colored noise.
