A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions

摘要

We study the loss, recovery, and preservation of differentiability oftime-dependent large deviation rate functions. This study is motivated bymean-field Gibbs-non-Gibbs transitions. The gradient of the rate-functionevolves according to a Hamiltonian flow. This Hamiltonian flow is used toanalyze the regularity of the time dependent rate function, both for Glauberdynamics for the Curie-Weiss model and Brownian dynamics in a potential. Wehereby create a unifying framework for the treatment of mean-fieldGibbs-non-Gibbs transitions, based on Hamiltonian dynamics and viscositysolutions of Hamilton-Jacobi equations.