Reduction of Variables and Processes in Macrodynamics

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Abstract
It is shown that the projection-operator method in the Heisenberg picture in non-equilibrium statistical mechanics can be extended to formulate the reduction of macrovariables in non-Hamiltonian systems far from thermal equilibrium whose time evolution is described by either stochastic or deterministic equations. Mori's scaling method for the reduction of processes is used to single out the long-time behavior characteristic of the relevant set of macrovariables. As illustrations, Haken's model for the coupling between a system and reservoirs and Edelstein's model for biochemical reactions near a critical point are studied from this new point of view. Thus it is shown that the Ginzburg-Landau type nonlinear equations for the fluctuations of the critical modes hold if α= β, and this method is more useful than the reductive-perturbation method.

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