Application of the Markov chain tree theorem to a system with timescale separation in its transition rates
No general framework exists to solve master equations, which describe the microscopic dynamics of Markov processes and are widely used to model stochastic systems, particularly those far from equilibrium. One method, normally intractable, follows from the Markov chain tree theorem, a result in graph theory that expresses the steady-state probability distribution of a Markovian system in terms of its transition graph. Inspired by recent work that shows the use of this method for Arrhenius systems in a low-temperature regime, we devise a scheme to find the steady-state probability distribution of a system that instead exhibits a natural timescale separation in its microscopic transition rates: two run-and-tumble random walkers which ‘run’ much more often than they ‘tumble’.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..