We consider a general system of n noninteracting identical particles whichevolve under a given dynamical law and whose initial microstates are a prioriindependent. The time evolution of the n-particle average of a bounded functionon the particle microstates is then examined in the large n limit. Using thetheory of large deviations, we show that if the initial macroscopic average isconstrained to be near a given value, then the macroscopic average at a giventime converges in probability, as n goes to infinity, to a value givenexplicitly in terms of a canonical expectation. Some general features of theresulting deterministic curve are examined, particularly in regard tocontinuity, symmetry, and convergence.
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