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

TL;DR

This paper links relative entropy to free energy changes in equilibrium and nonequilibrium fluctuations of macromolecules, providing a physical interpretation of information-theoretic measures in thermodynamics.

Contribution

It demonstrates that relative entropy naturally represents free energy differences in both equilibrium and nonequilibrium conformational fluctuations of macromolecules.

Findings

Relative entropy quantifies free energy differences in fluctuations.

The approach applies to isothermal macromolecular systems.

Provides physical interpretation of information theory in thermodynamics.

Abstract

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.