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

We study the loss, recovery, and preservation of differentiability time-dependent large deviation rate functions. This is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient rate-function evolves according to a Hamiltonian flow. flow used analyze regularity function, both for Glauber dynamics Curie-Weiss model Brownian in potential. extend variational approach this problem order include trajectories with finite lifetime closed domains boundary. leads new phenomena, such recovery smoothness. hereby create unifying transitions, based on viscosity solutions Hamilton-Jacobi equations.