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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Mean-field limit and large deviation for chemical
reaction kinetics from Hamiltonian viewpoint and u
pwind scheme - Jian-Guo Liu (Duke University)
DTSTART;TZID=Europe/London:20220526T111500
DTEND;TZID=Europe/London:20220526T121500
UID:TALK173624AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173624
DESCRIPTION:Chemical reactions can be modeled by random time-c
hanged Poisson processes. To characterize macrosco
pic behaviors in the large volume limit\, the law
of large numbers in the path space determines a me
an-field limit nonlinear reaction rate equation de
scribing the dynamics of the concentration of spec
ies\, while the WKB expansion for the chemical mas
ter equation yields a Hamilton-Jacobi equation (HJ
E) and the Lagrangian gives the good rate function
in the large deviation principle. By regarding ch
emical master equation as an upwind scheme\, whose
structure is preserved in HJE\, we give another p
roof for the mean-field limit reaction rate equati
on. \;We decompose the mean-field reaction ra
te equation into a conservative part and a dissipa
tive part in terms of the stationary solution to H
JE. This stationary solution is used to determine
the energy landscape and thermodynamics for genera
l chemical reactions. The associated energy dissip
ation law at both the mesoscopic and macroscopic l
evels is proved together with a passage from the m
esoscopic to macroscopic one. A non-convex energy
landscape emerges from the convex mesoscopic relat
ive entropy functional in the large volume limit\,
which picks up the non-equilibrium features. &nbs
p\;Furthermore\, we use a reversible Hamiltonian t
o study a class of non-equilibrium enzyme reaction
s\, which reduces the conservative-dissipative dec
omposition to an Onsager-type strong gradient flow
\, and a modified time reversed least action path
serves as the transition paths between multiple no
n-equilibrium steady states with associated path a
ffinities. In chemical reaction detailed balance c
ase\, \;the comparison principle for HJE prev
ents a class of initial distribution converging to
the equilibrium. This is a joint work with Yuan G
ao at Purdue University.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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