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SUMMARY:Mean-field limit and large deviation for chemical reaction kinetic
 s from Hamiltonian viewpoint and upwind scheme - Jian-Guo Liu (Duke Univer
 sity)
DTSTART:20220526T101500Z
DTEND:20220526T111500Z
UID:TALK173624@talks.cam.ac.uk
DESCRIPTION:Chemical reactions can be modeled by random time-changed Poiss
 on processes. To characterize macroscopic behaviors in the large volume li
 mit\, the law of large numbers in the path space determines a mean-field l
 imit nonlinear reaction rate equation describing the dynamics of the conce
 ntration of species\, while the WKB expansion for the chemical master equa
 tion yields a Hamilton-Jacobi equation (HJE) and the Lagrangian gives the 
 good rate function in the large deviation principle. By regarding chemical
  master equation as an upwind scheme\, whose structure is preserved in HJE
 \, we give another proof for the mean-field limit reaction rate equation. 
 &nbsp\;We decompose the mean-field reaction rate equation into a conservat
 ive part and a dissipative part in terms of the stationary solution to HJE
 . This stationary solution is used to determine the energy landscape and t
 hermodynamics for general chemical reactions. The associated energy dissip
 ation law at both the mesoscopic and macroscopic levels is proved together
  with a passage from the mesoscopic to macroscopic one. A non-convex energ
 y landscape emerges from the convex mesoscopic relative entropy functional
  in the large volume limit\, which picks up the non-equilibrium features. 
 &nbsp\;Furthermore\, we use a reversible Hamiltonian to study a class of n
 on-equilibrium enzyme reactions\, which reduces the conservative-dissipati
 ve decomposition to an Onsager-type strong gradient flow\, and a modified 
 time reversed least action path serves as the transition paths between mul
 tiple non-equilibrium steady states with associated path affinities. In ch
 emical reaction detailed balance case\, &nbsp\;the comparison principle fo
 r HJE prevents a class of initial distribution converging to the equilibri
 um. This is a joint work with Yuan Gao at Purdue University.
LOCATION:Seminar Room 1\, Newton Institute
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