Monte Carlo sampling in path space: Calculating time correlation functions by transforming ensembles of trajectories
in: Proceedings of the Monte Carlo method in the Physical Sciences: Celebrating the 50th anniversary of the Metropolis algorithm, AIP Conference proceedings; AIP: Melville, NY , 690 (2003), p. 192
Computational studies of processes occurring in complex systems with meta-stable states are often complicated by a wide separation of time scales. Such processes can be studied with transition path sampling, a computational methodology based on an importance sampling of reactive trajectories capable of bridging this time scale gap. Within this perspective, ensembles of trajectories can be sampled and manipulated in close analogy to standard techniques of statistical mechanics. In particular, the population time correlation functions appearing in the expressions for transition rate constants can be expressed using free energy differences between ensembles of trajectories. Here we calculate such free energy differences with thermodynamic integration, which, in effect, corresponds to reversibly changing between ensembles of trajectories. Further we show how to calculate free energy differences in path space from non-equilibrium, fast switching simulations based on the recently discovered theorem of Jarzynski.
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