We consider the quasi-deterministic behavior of systems with a large number, n, of deterministically interacting constituents. This work extends the results of a previous paper [J. Statist. Phys. 99:1225-1249 (2000)] to include vector-valued observables on interacting systems. The approach used here, however, differs markedly in that a level-1 large deviation principle (LDP) on joint observables, rather than a level-2 LDP on empirical distributions, is employed. As before, we seek a mapping psi(iota) on the set of (possibly vector-valued) macrostates such that, when the macrostate is given to be a(0) at time zero, the macrostate at time t is psi(iota)(a(0)) with a probability approaching one as n tends to infinity. We show that such a map exists and derives from a generalized dynamic free energy function, provided the latter is everywhere well defined, finite, and differentiable. We discuss some general properties of psi(iota) relevant to issues of irreversibility and end with an example of a simple interacting lattice, for which an exact macroscopic solution is obtained. [References: 27]
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