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Non-Equilibrium is Different

Non-equilibrium and equilibrium fluid systems differ due to the existence of long-range correlations in non-equilibrium that are not present in equilibrium, except at critical points. Here we examine fluctuations of the temperature, of the pressure tensor, and of the heat current in a fluid maintained in a non-equilibrium stationary state (NESS) with a fixed temperature gradient, a system where the non-equilibrium correlations are especially long ranged. For this particular NESS our results show that (1) The mean-squared fluctuations in non-equilibrium differ markedly in their system size scaling compared to their equilibrium counterparts and (2) There are large, nonlocal, correlations of the normal stress in this NESS. These terms provide important corrections to the fluctuating normal stress in linearized Landau-Lifshitz fluctuating hydrodynamics.