Nonequilibrium fluctuation-dissipation theorem of Brownian dynamics

Studying the Brownian motion of a system driven by an external control from one macroscopic state to another macroscopic state, this paper presents the derivation of a nonlinear fluctuation-dissipation theorem (FDT). The new FDT relates the nonequilibrium work to the equilibrium free-energy difference in a very simple manner. It is valid wherever the Brownian dynamics is applicable. It recovers the well-known Crooks fluctuation theorem (CFT) within the quasiequilibrium regime where the dissipative work is nearly zero. It will also be shown that the CFT's fundamental assumption of microscopic reversibility is not obeyed in experiments such as mechanically unfolding biological molecules, in which the external driving forces depend on the system's coordinates.