Canonical Structure of Irreversible Markov Chains and Applications

Wednesday, August 9, 2017 - 2:00pm - 2:45pm
Vincent 215
Johannes Zimmer (University of Bath)
We consider dynamical fluctuations in systems described by Markov chains, and discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible Markov chains, Onsager theory, and macroscopic fluctuation
theory. For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. We
discuss the resulting variational structure, which leads to generalised gradient flows. It is shown that various physically
natural splittings can be introduced, which can help to derive applications such as an understanding of acceleration of convergence to equilibrium and dissipation bounds. This is joint work with Marcus Kaiser (Bath) and Rob Jack (Bath Physics).