2018-03-28
10:15 at HCP F 43.4

Gradient and GENERIC structures from flux large deviations

Michiel Renger

Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

In statistical mechanics, the free energy of a macroscopic system is usually derived from the large deviations of a corresponding random microscopic system. In the same spirit, one can often derive a free-energy-driven gradient structure behind the macroscopic evolution from large deviations; recent developments show the same principle for GENERIC systems. In search for deeper thermodynamic structure, we study microscopic systems with an additional flux random variable, coupled to the state variable via a continuity equation. From the corresponding large deviations we then derive a gradient or GENERIC structure, but now in the space of fluxes. By the very nature of these systems, the free energy will depend only indirectly on the flux, via the state variable. We shall see that this implies a direct connection with the state space structure. This connection reveals interesting new structures in flux space, and also explains why the state space gradient or GENERIC structure is always of a certain form.