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 In 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) = U(x) + k(B)T ln p(ness)(x), where p,,e,,(X) is the NESS probability density in the phase space of the macromolecule and U(x) is its internal potential function. Psi = f 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)fP(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.