Entropic Gradient flows on the Wasserstein space via large deviations from thermodynamic limits

In a seminal work, Jordan, Kinderlehrer and Otto proved that the Fokker-Planck equation can be described as a gradient flow of the free energy functional in the Wasserstein space, bringing this way the underlying particle interpretation of the diffusion phenomenon in the forefront. The aim of the talk is to convince the audience that it is possible to retrieve this natural (from a statistical mechanics point of view) coupling of functional and metric, by studying the large deviations of particle models. The talk will contain an introduction to the Wasserstein space and its geometric properties, a brief discussion of large deviations and the presentation of my work on the subject.