Talk by Michiel Renger

The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 in lecture room K3. The talk will be given by Michiel Renger. Please see the details below.

Speaker: Michiel Renger
Title: Macroscopic Fluctuation Theory on discrete spaces

Abstract: Often thermodynamical phenomena are described microscopically by a randomly evolving particle system, or macroscopically by an evolution equation, and the two levels of description are connected by sending the number of particles to infinity. Onsager and Machlup postulated that microscopic systems in detailed balance (reversible Markov process) behave as a gradient flow on the macroscopic level. This principle is now well-understood and can be made precise via the theory of large deviations. In order to understand the behaviour of non-equilibrium systems (not in detailed balance/nonreversible), one commonly studies large deviations of particle densities and fluxes. Classically one can decompose the dynamics into a gradient flow component (dissipating free energy) and a Hamiltonian component (conserving energy). Such decomposition becomes more difficult on discrete spaces, and a choice needs to be made: either to decompose fluxes or to decompose forces into dissipative and conservative parts. Decomposing fluxes is consistent with the GENERIC formalism, which is only rarely applicable to dynamics on discrete spaces. Decomposing forces is more consistent with Macroscopic Fluctuation Theory, and yields a framework that is sufficiently general to apply to, for example zero-range processes, boundary-driven systems and chemical reactions.

This work lies on the boundary between probability, analysis and physics, but I will mostly focus on the analysis and physics part.