Nonequilibrium Markov processes conditioned on large deviations

Abstract

We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used in the conditioning is a large deviation-type event, characterized by a convex rate function. Under this assumption, we construct the driven process via a generalization of Doob's $h$-transform, used in the context of bridge processes, and show that this process is equivalent to the conditioned process in the long-time limit. The notion of equivalence that we consider is based on the logarithmic equivalence of path measures and implies that the two processes have the same typical states. In constructing the driven process, we also prove equivalence with the so-called exponential tilting of the Markov process, which is used with importance sampling to simulate rare events, and which gives rise, from the point of view of statistical mechanics, to a nonequilibrium version of the canonical ensemble. Other links between our results and the topics of bridge processes, quasi-stationary distributions, stochastic control, and conditional limit theorems are mentioned.

46 pages, 1 figure; v2: some typos corrected; v3: tiny typos corrected, same as published version

References in corpus (10)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuations and response of nonequilibrium states
• A numerical approach to large deviations in continuous-time
• Steady state statistics of driven diffusions
• Fluctuation relations in simple examples of non-equilibrium steady states
• Nonlinear response and fluctuation dissipation relations
• Invariant quantities in shear flow
• Properties of a non-equilibrium heat bath
• Heterogeneity-induced large deviations in activity and (in some cases) entropy production

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