  We consider a general system of n noninteracting identical particles which
evolve under a given dynamical law and whose initial microstates are a priori
independent. The time evolution of the n-particle average of a bounded function
on the particle microstates is then examined in the large n limit. Using the
theory of large deviations, we show that if the initial macroscopic average is
constrained to be near a given value, then the macroscopic average at a given
time converges in probability, as n goes to infinity, to a value given
explicitly in terms of a canonical expectation. Some general features of the
resulting deterministic curve are examined, particularly in regard to
continuity, symmetry, and convergence.
