Relative Entrop: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

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Abstract
Using a one-dimensional system as an illustration, we demonstrate that the relative entropy from information theory has a natural role in equilibrium and nonequilibrium statistical mechanics. We identify it as the free energy difference associated with a fluctuating density in equilibrium, and associated with the distribution deviate from the equilibiurm in nonequilibrium relaxation. This result can be generalized to any other isothermal systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the mathematical results with clear physical interpretations.

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