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# Trajectory reweighting

##### In a collaboration with Patrick Warren of Unilever R&D, I have been exploring advanced computer simulation methods for use in non-equilibrium stochastic systems. For equilibrium systems, many sophisticated simulation methods exist, thanks to our knowledge of the Boltzmann factor, which tell us the relative probabilities of microstates, for the system in its steady state.

For non-equilibrium systems we do not have such knowledge. However, if we know the dynamical rules that are used to run the simulation, we can work out the probability of obtaining a particular sequence of states, or trajectory. Knowing this probability allows us to devise "trajectory reweighting" schemes in which we bias the dynamics towards outcomes that are scientifically interesting, while reweighting afterwards to obtain the correct statistics. We have explored this idea in the context of calculating parameter sensitivities in kinetic Monte Carlo simulations, and also for computing response coefficients in Brownian dynamics simulations. Recently, we have been investigating whether it is also useful for sampling the steady-state phase space density.

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