Michiel Renger: Variational Structures Beyond Gradient Flows

Joint work with Upanshu Sharma (FU Berlin) & Robert I.A. Patterson (WIAS Berlin)

Motivated but not restricted to large deviations of stochastic particle systems, we study a general class of action functionals that are minimised by a given evolution. It is known that for the special case of reversible systems, these functionals are natural variational formulations of a gradient flow, whereas irreversible systems will require a more general structure. We show in a general setting that the action can always be decomposed into a reversible/gradient flow part and a "purely irreversible" part. For specific examples this purely irreversible part displays solutions with periodic orbits or even Hamiltonian dynamics.

Applications include zero range processes, complex balanced chemical reactions, lattice gases and recently also models with open boundaries.