ACTION PRINCIPLE IN STATISTICAL DYNAMICS

We discuss a least-action principle characterizing ensemble-averages i n statistical dynamics, based upon ''effective actions'' defined as in quantum field-theory. These generalize to all system variables the On sager-Machlup actions of thermodynamic fluctuation theory. In the stat istical steady-state, the variational principles discussed are related to the ''thermodynamical formalism'' for chaotic dynamical systems. N on-perturbative methods of field-theory can be applied to approximate the effective actions: instantons, 1/N-expansion, Hartree-Fock, Raylei gh-Ritz, etc. In particular, the Rayleigh-Ritz method is shown to be c losely related to traditional moment-closure schemes. Some concrete ap plications of the variational methods are outlined, e.g., to free deca y of homogeneous, isotropic Navier-Stokes turbulence at high Reynolds number. ''Fluctuation-dissipation relations'' are obtained for the str ength of turbulence-generated eddy noise in terms of mean dissipation Characteristics. The relation of the effective action to dissipation a nd transport characteristics was already noted by Onsager, who pointed out that the associated variational principles generalize the hydrody namic least-dissipation principle of Rayleigh. We briefly discuss the application of such principles to pattern-selection far from equilibri um.