Anomalous pressure in fluctuating shear flow

We investigate how the pressure in fluctuating shear flow depends on the shear rate S and on the system size L by studying fluctuating hydrodynamics under shear conditions. We derive anomalous forms of the pressure for two limiting values of the dimensionless parameter λ=SL²/ν, where ν is the kinematic viscosity. In the case λ≪1, the pressure is not an intensive quantity because of the influence of the long-range spatial correlations of momentum fluctuations. In the other limit λ≫1, the long-range correlations are suppressed at large distances, and the pressure is intensive. In this case, however, there is the interesting effect that the nonequilibrium correction to the pressure is proportional to S^3/2, which was previously obtained with the projection operator method [K. Kawasaki and J. D. Gunton, Phys. Rev. A 8, 2048 (1973)].