Abstract: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 extend the variational approach to this problem of time-dependent regularity in order to include Hamiltonian trajectories with a finite lifetime in closed domains with a boundary. This leads to new phenomena, such a recovery of smoothness. We hereby create a new and unifying approach for the study of mean-field Gibbs-non-Gibbs transitions, based on Hamiltonian dynamics and viscosity solutions of Hamilton-Jacobi equations.

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中文翻译：

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关于平均场 Gibbs-non-Gibbs 转换的 Hamilton-Jacobi 观点

摘要：我们研究了瞬态大偏差率函数的可微性的损失、恢复和保持。这项研究的动机是平均场 Gibbs-non-Gibbs 转换。速率函数的梯度根据哈密顿流演化。该哈密顿流用于分析随时间变化的速率函数的规律性，包括 Curie-Weiss 模型的 Glauber 动力学和势中的 Brownian 动力学。我们将变分方法扩展到这个与时间相关的规律性问题，以便在具有边界的封闭域中包含具有有限寿命的哈密顿轨迹。这会导致新现象，例如平滑度的恢复。我们在此创建了一种新的统一方法来研究平均场 Gibbs-non-Gibbs 跃迁，

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