A Hamilton--Jacobi point of view on mean-field Gibbs-non-Gibbs transitions
- Kraaij, Richard
- Redig, Frank
- van Zuijlen, Willem
2010 Mathematics Subject Classification
- 49L99 60F10 82C22 82C27
- Hamiltonian dynamics, Hamilton-Jacobi equation, mean-field models, large deviation principle, Gibbs versus non-Gibbs, dynamical transition, global minimisers of rate functions
We study the loss, recovery, and preservation of differentiability of time-dependent 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.