Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in
terms of Markov jump processes, we identify the scaling conditions that ensure the …

We formulate a class of mean field games on a finite state space with variational principles
resembling those in continuous-state mean field games. We construct a controlled continuity …

We formulate and compute a class of mean-field information dynamics for reaction-diffusion
equations. Given a class of nonlinear reaction-diffusion equations and entropy type …

We present a data-driven point of view for rare events, which represent conformational
transitions in biochemical reactions modeled by overdamped Langevin dynamics on …

We study a class of variational problems for regularized conservation laws with Lax's
entropy-entropy flux pairs. We first introduce a modified optimal transport space based on …

In this paper, we construct structure preserving schemes for solving Fokker–Planck
equations associated with irreversible processes. The proposed method is first order in time …

This paper reinterprets the Freidlin–Wentzell variational construction of the rate function in
the large deviation principle for invariant measures from the weak KAM perspective …

The interplay between stochastic processes and optimal control has been extensively
explored in the literature. With the recent surge in the use of diffusion models, stochastic …

Macroscopic equations arising out of stochastic particle systems in detailed balance (called
dissipative systems or gradient flows) have a natural variational structure, which can be …

Chemical reactions can be modeled by a random time-changed Poisson process on
countable states. The macroscopic behaviors, such as large fluctuations, can be studied via …