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Free keywords:
Transition path theory · Markov chains · Time-inhomogeneous process ·
Periodic driving · Finite-time dynamics
Abstract:
Given two distinct subsets A, B in the state space of some dynamical system, transition
path theory (TPT) was successfully used to describe the statistical behavior of
transitions from A to B in the ergodic limit of the stationary system.We derive generalizations
of TPT that remove the requirements of stationarity and of the ergodic limit
and provide this powerful tool for the analysis of other dynamical scenarios: periodically
forced dynamics and time-dependent finite-time systems. This is partially
motivated by studying applications such as climate, ocean, and social dynamics. On
simple model examples, we show how the new tools are able to deliver quantitative
understanding about the statistical behavior of such systems.We also point out explicit
cases where the more general dynamical regimes show different behaviors to their stationary
counterparts, linking these tools directly to bifurcations in non-deterministic
systems.
