Statistical mechanics of stationary states. IV. Far-from-equilibrium stationary states and the regression of fluctuations

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Abstract
The authors present a microscopic theory for the averages of any dynamical variable and in particular of fluctuations in nonequilibrium stationary states that are arbitrarily far from equilibrium, as long as the macroscopic gradients are sufficiently small. It is argued that the dynamics of the fluctuations are governed by the linearized macroscopic equations of motion (analogous to Onsager's hypotheses for equilibrium fluctuations). The fluctuation-dissipation theorem is examined and it is found that it does not hold in its equilibrium form. The authors find that the dissipation does not contain an important part of the information about the fluctuation, and attempt an interpretation of this fact.