*From Particles to Non-equilibrium Thermodynamics: A New Perspective*

**Michiel Renger**

Technical University Eindhoven

Department of Mathematics and Computer Science

`d.r.m.renger@tue.nl`

**Abstract**: Since a famous article by Jordan, Otto and
Kinderlehrer, it is well-known that the Fökker-Planck equation can be
described as a gradient flow of free energy in the Wasserstein metric. It is
common in gradient flow structures that the metric can be interpreted as the
dissipation or energy loss of the system. However, it is not immediately clear
how the Wasserstein metric can be viewed as such. To understand this, we
switch to a particle system that can be interpreted as a microscopic model for
the continuum equation. It turns out that the Wasserstein gradient flow is
closely related to the large-deviation behaviour of such systems.