Transition path sampling stochastic dynamics

Crooks, G. E. Chandler, D., Efficient transition path sampling for nonequilibrium stochastic dynamics, Phys. Rev. E 2001, 64, 026109/1 -4... 

The perspective exploited by transition path sampling, namely, a statistical description of pathways with endpoints located in certain phase-space regions, was hrst introduced by Pratt [27], who described stochastic pathways as chains of states, linked by appropriate transition probabilities. Others have explored similar ideas and have constructed ensembles of pathways using ad hoc probability functionals [28-35]. Pathways found by these methods are reactive, but they are not consistent with the true dynamics of the system, so that their utility for studying transition dynamics is limited. Trajectories in the transition path ensemble from Eq. (1.2), on the other hand, are true dynamical trajectories, free of any bias by unphysical forces or constraints. Indeed, transition path sampling selects reactive trajectories from the set of all trajectories produced by the system s intrinsic dynamics, rather than generating them according to an artificial bias. This important feature of the method allows the calculation of dynamical properties such as rate constants. 

The transition path sampling techniques we have described assume that an initial reactive pathway is available. Generating such a pathway is therefore an important step in applying the method. In the simplest cases, a trajectory connecting A and B can be obtained by running a long molecular dynamics (or stochastic dynamics) simulation. For most applications, however, the... 

---