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- ItemA Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Kraaij, Richard C.; Redig, Frank; Zuijlen, Willem B. vanWe study the loss, recovery, and preservation of differentiability of timedependent large deviation rate functions. This study is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient of the rate-function evolves according to a Hamiltonian flow. This Hamiltonian flow is used to analyze the regularity of the time dependent rate function, both for Glauber dynamics for the Curie-Weiss model and Brownian dynamics in a potential. We hereby create a unifying framework for the treatment of mean-field Gibbs-non-Gibbs transitions, based on Hamiltonian dynamics and viscosity solutions of Hamilton-Jacobi equations.