The stochastic H-theorem

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Abstract
The stochastic analogue of the generalized H‐theorem is formulated for multidimensional, time homogeneous diffusion processes which asymptotically are characterized by an invariant probability distribution. It applies to both isolated and open thermodynamic systems, the latter being characterized by rotational probability currents. The physical mechanism for the monotonic behavior of the stochastic H‐function in time is linked to the decay of statistical correlations between a given nonequilibrium state and those through which the system passes at successive instants in time.