4 - Work Distributions from Hamiltonian Trajectories

Summary

For time-dependent driving, the key concepts of time-reversed and backward protocols are introduced. The reversibility of Hamiltonian dynamics is shown to imply that work is antisymmetric with respect to time-reversal. Integral fluctuation relations are introduced as a general property of certain distributions. For the work distributions, this yields the Jarzynski relation, which expresses free-energy differences as a particular nonlinear average over nonequilibrium work. Various limiting cases such as slow driving and the apparent counterexample of free expansion of a gas are discussed. The Bochkov–Kuzovlev relation is shown to be another variant of such an integral fluctuation relation. The Crooks fluctuation relation yields a symmetry of the work distributions for a forward and a backward process. As an important application, free energy differences and a free energy landscape based on exploiting the Hummer–Szabo relation are recovered as illustrated with experimental data for the unfolding of biopolymers.