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Thermal fluctuations in non-equilibrium steady states generically lead topower law decay of correlations for conserved quantities. Embedded bodies whichconstrain fluctuations in turn experience fluctuation induced forces. Wecompute these forces for the simple case of parallel slabs in a drivendiffusive system. The force falls off with slab separation $d$ as $k_B T/d$ (attemperature $T$, and in all spatial dimensions), but can be attractive orrepulsive. Unlike the equilibrium Casimir force, the force amplitude isnon-universal and explicitly depends on dynamics. The techniques introduced canbe generalized to study pressure and fluctuation induced forces in a broadclass of non-equilibrium systems.

Fluctuation Induced Forces in Non-equilibrium (Diffusive) Dynamics