  Long-ranged correlations generically exist in non-equilibrium fluid systems.
In the case of a non-equilibrium steady state caused by a temperature gradient
the correlations are especially long-ranged and strong. The anomalous light
scattering predicted to exist in these systems is well-confirmed by numerous
experiments. Recently the Casimir force or pressure due to these fluctuations
or correlations have been discussed in great detail. In this paper the notion
of a Casimir work is introduced and a novel way to measure the non-equilibrium
Casimir force is suggested. In particular, the non-equilibrium Casimir force is
related to a non-equilibrium heat and not, as in equilibrium, to a volume
derivative of an average energy. The non-equilibrium work fluctuations are
determined and shown to be very anomalous compared to equilibrium work
fluctuations. The non-equilibrium work distribution is also computed, and
contrasted to work distributions in systems with short-range correlations.
Again, there is a striking difference in the two cases. Formal theories of work
and work distributions in non-equilibrium steady states are not explicit enough
to illustrate any of these interesting features.
