Since Gibbs, thermodynamic phase space has been known to carry a distinguished one-form defining a contact structure—a geometric framework that provides a concise formulation of equilibrium thermodynamics and is an object of ongoing study in modern contact topology.The Fokker–Planck equation—viewed as a heat equation associated with a Witten Laplacian—governs non-equilibrium relaxation processes. In this talk, I will discuss several links between these two themes. As a guiding example, I will use the thermodynamic limit of the mean-field Ising model. Joint work with Michael Entov and Lenya Ryzhik.
