Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Work

Abstract

Applying the method from recently developed fluctuation theorems to the stochastic dynamics of single macromolecules in ambient fluid at constant temperature, we establish two Jarzynski-type equalities: (1) between the log-mean-exponential (LME) of the irreversible heat dissiption of a driven molecule in nonequilibrium steady-state (NESS) and \(\ln P^{ness}(x)\), and (2) between the LME of the work done by the internal force of the molecule and nonequilibrium chemical potential function \(\mu^{ness}(x)\) \(\equiv U(x)+k_BT\ln P^{ness}(x)\), where \(P^{ness}(x)\) is the NESS probability density in the phase space of the macromolecule and \(U(x)\) is its internal potential function. \(\Psi\) = \(\int\mu^{ness}(x)P^{ness}(x)dx\) is shown to be a nonequilibrium generalization of the Helmholtz free energy and \(\Delta\Psi\) = \(\Delta U-T\Delta S\) for nonequilibrium processes, where \(S\) \(=-k_B\int P(x)\ln P(x)dx\) is the Gibbs entropy associated with \(P(x)\). LME of heat dissipation generalizes the concept of entropy, and the equalities define thermodynamic potential functions for open systems far from equilibrium.