In many stochastic systems one is interested in understanding the critical transitions the system can take between different dynamical regimes. In this talk, I will first give an overview of some systems with interesting transition behaviour such as systems containing human agents.
We will assume that the dynamics of the system can be modelled by a Markov process that is potentially time-dependent and out-of-equilibrium.
Then I will introduce you to Transition Path Theory for Markov Processes in equilibrium and how we extended it for Markov processes that are out of equilibrium. Transition Path Theory is a method for getting statistics of the transitions between two subsets of the state space, such as the rate of transitions, the density of transition paths, and the dominant transition channels.