|Date||Nov 25, 2022|
In this thesis, we investigated the metastability of non-reversible Langevin dynamics.
The first topic is the precise estimation of the expectation of transition time, which is called the Eyring-Kramers formula. Compared to the gradient model, our result reveals that the metastable transition of the non-reversible dynamics occurs faster than that of the reversible ones. Proof of the Eyring-Kramer formula is based on a potential theoretic approach estimating the capacity between metastable valleys. We developed a novel method to estimate capacity without relying on variational principles such as Dirichlet's and Thomson's principles. In addition, we also explain the Markov chain model reduction of the non-reversible dynamics which provides the full description of successive transitions when there are multiple global minima.
Finally, we introduce the analysis of the energy landscape of the Curie-Weiss-Potts model which is an example of a dynamics on complex potential function so that complex metastability investigated above indeed occurs.