TY - JOUR
T1 - Hamilton Dynamics in Chemical Reactions: The Maupertuis Principle, Transition Paths and Energy Landscape
AU - Gao , Yuan
AU - Zhou , Yufan
JO - Communications in Mathematical Analysis and Applications
VL - 3
SP - 245
EP - 288
PY - 2023
DA - 2023/09
SN - 2
DO - http://doi.org/10.4208/cmaa.2023-0003
UR - https://global-sci.org/intro/article_detail/cmaa/22014.html
KW - Large deviation principle, thermodynamic limit, transition time, energy barriers, infinite time horizon.
AB - <p style="text-align: justify;">In this paper, we explore the Hamilton structures in non-equilibrium
chemical reactions, which is modeled as a random time-changed Poisson process on countable states. Transition paths between multiple steady states in
a chemical reaction is a rare event that can be characterized via the large deviation principle. Compared with the Hamilton principle, we use the Maupertuis
principle to compute the transition paths and the associated energy barriers,
i.e., the rate function in the large deviation principle. Based on the corresponding stationary Hamilton-Jacobi equation, we select a proper stationary viscosity
solution, which in general is not unique, to explicitly compute the energy barriers and the associated optimal control that realizes a transition path. Using
one-dimensional example, we characterize the energy barriers for chemical reactions using a geometric quantity in the phase plane. We also compare the
reaction barriers with the one in the diffusion approximation and show that
the global energy landscape and energy barriers for non-equilibrium chemical
reactions are quite different with its diffusion approximation.</p>