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

Details Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

2000-07-08

arxiv.org/abs/math-ph/0007010v2

Physical Review E, Vol. 63, pp. 042103/1-042103/4 (2001)

Physics

Mathematical Physics

5 pages

Scientific paper

10.1103/PhysRevE.63.042103

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.

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