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In this letter we consider the fluctuation induced force exerted between two plates separated by a distance L in a fluid with a temperature gradient. We predict that, for a range of distances L, this non-equilibrium force is anomalously large compared to other Casimir forces. The physical reason is that correlations in a non-equilibrium fluid are generally of longer range than other correlations, even than those near an equilibrium critical point. This giant Casimir force is related to a divergent Burnett coefficient that characterizes an Onsager cross effect between the pressure and the temperature gradient. The predicted Casimir force should be detectable with currently available experimental techniques.

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Correlations in fluids in nonequilibrium steady states are long range. Hence, finite-size effects have important consequences in the nonequilibrium thermodynamics of fluids. One consequence is that nonequilibrium temperature fluctuations induce nonequilibrium Casimir-like pressures proportional to the square of the temperature gradient. Hence, fluctuations cause a breakdown of the concept of local thermal equilibrium. Furthermore, transport coefficients become dependent on boundary conditions and on gravity. Thus nonequilibrium fluctuations affect some traditional concepts in nonequilibrium thermodynamics.