A differential fluctuation theorem

We derive a nonequilibrium thermodynamics identity (the "differential fluctuation theorem") that connects forward and reverse joint probabilities of nonequilibrium work and of arbitrary generalized coordinates corresponding to states of interest. This identity allows us to estimate the free energy difference between domains of these states. Our results follow from a general symmetry relation between averages over nonequilibrium forward and backward path functions derived by Crooks Crooks, G. E. Phys. Rev. E 2000, 61, 2361-2366]. We show how several existing nonequilibrium thermodynamic identities can be obtained directly from the differential fluctuation theorem. We devise an approach for measuring conformational free energy differences, and we demonstrate its applicability to the analysis of molecular dynamics simulations by estimating the free energy difference between two conformers of the alanine dipeptide model system. We anticipate that these developments can be applied to the analysis of laboratory experiments.