Gradient Flow of the Free Energy of Infinite Volume Interacting Spin System
A talk in the Oberseminar Analysis series by
Ronan Herry
| Abstract: | A seminal result of Jordan, Kinderlehrer and Otto states that Fokker Planck equations on Euclidean spaces can be interpreted as a gradient flow of the relative entropy through optimal transport. In the first part of the talk, I will briefly recall this theory in the usual setting and highlight some iconic generalisations and their consequences.
In the second part, based on a joint work with Thomas Leblé, I will present some of the ideas we used to generalise this result to the setting of interacting spin systems, where the underlying space is a countable product of compact Riemannian manifold, and the range of the interaction is potentially infinite. In particular, I will define the free energy, and the infinite-volume diffusion, partial differential equation and gradient flow that model this situation and show they are related through an Evolution Variational Inequality. Our approach establishes in particular that at high enough temperature the free energy decays exponentially fast along the dynamic, which is new. Meeting-ID: 622 2841 8411 Passwort: 058508 https://uni-bielefeld.zoom-x.de/j/62228418411?pwd=bkNteGxqMGFRemZhOWRwek1tNGtkUT09 Within the CRC this talk is associated to the project(s): A8 |