Nonequilibrium potential function of chemically driven single macromolecules via Jarzynski-type Log-Mean-Exponential Heat

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) identical with U(x) + k(B)T 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 = integral mu(ness)(x) P(ness)(x) dx is shown to be a nonequilibrium generalization of the Helmholtz free energy and DeltaPsi = DeltaU - TDeltaS for nonequilibrium processes, where S = - kB integralP(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.