Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory |
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Authors: | Brian R. La Cour William C. Schieve |
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Affiliation: | (1) Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems and Department of Physics, University of Texas at Austin, Austin, Texas, 78712 |
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Abstract: | 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, y, then the macroscopic average at time t converges in probability as n to a value t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence. |
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Keywords: | determinism causality large deviation theory many-particle systems fluctuations nonequilibrium statistical mechanics kinetic theory |
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