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CATEGORIES:DAMTP Statistical Physics and Soft Matter Seminar
SUMMARY:Path large deviations for kinetic theories: beyond
the Boltzmann\, the Landau\, the Balescu—Lenard—G
uernsey\, and the weak turbulence kinetic equation
s + Rare event dynamics applied to climate models
- Freddy Bouchet\, ENS Paris
DTSTART;TZID=Europe/London:20230207T130000
DTEND;TZID=Europe/London:20230207T140000
UID:TALK193459AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/193459
DESCRIPTION:Online seminar \n\nIn many physical systems one se
eks to describe effectively mesoscopic or macrosco
pic variables. Kinetic theories and kinetic equati
ons are examples where the average mesoscopic dyna
mics is obtained through very clear theoretical pr
ocedures and can possibly lead to mathematical pro
ofs\, for instance the Boltzmann equation for dilu
te gases\, the Landau or the Balescu—Guernsey—Lena
rd equations in plasma physics\, or the wave kinet
ic equation for weak turbulence theory. A few work
s go beyond the average evolution and describe\, f
or instance\, Gaussian fluctuations. However\, for
many physical systems\, rare events can be of imp
ortance\, and Gaussian fluctuations are not releva
nt. This is the case for instance if one wants to
understand the irreversibility paradox associated
to the kinetic equations\, or to understand the dy
namics that leads to rare events with big impact.
\nThe aim of this presentation is to describe rece
nt results where we derived explicitly the functio
nal that describes the path large deviations for t
he empirical measure of dilute gases\, plasma\, sy
stems of particles with long range interactions\,
and waves with weak interactions. The associated k
inetic equations (the average evolution) are then
either the Boltzmann\, the Landau\, the Balescu--L
enard—Guernsey\, or the weak turbulence kinetic eq
uations. After making the classic assumptions in
theoretical physics textbooks for deriving the kin
etic equation\, our derivation of the large deviat
ion functional is exact.\nThese path large deviati
on principles give a very nice and transparent new
interpretation of the classical irreversibility p
aradox. This new explanation is fully compatible w
ith the classical one\, but it gives a deeper insi
ght.\nAlthough this will not be the subject of thi
s talk\, I will take five to ten minutes to review
our current work to apply rare event algorithms f
or studying climate extreme events and abrupt tran
sitions.\n\nJoint works with Gregory Eyink\, Ouass
im Feliachi\, Jules Guioth and Yohei Onuki\n \nRef
erences:\nFor the large deviations associated to t
he Boltzmann equation (dilute gazes)\, and a gener
al introduction (published in J. Stat. Phys. in 20
20): F. Bouchet\, 2020\, Journal of Statistical Ph
ysics\, 181\, 515–550.\n \nFor the large deviation
s associated to the Landau equation (plasma below
the Debye length\, accepted for publication in J.
Stat. Phys. in March 2021): O. Feliachi and F. Bou
chet\, 2021\, Journal of Statistical Physics\, 183
\, 42.\n\nFor the large deviations associated with
the Balescu—Guernsey--Lenard equation (plasma and
systems with long range interactions): O. Feliach
i and F. Bouchet\, 2022\, Journal of Statistical P
hysics 186\, 22\, and arxiv:2105.05644\n \nFor the
large deviations associated with the weak turbule
nce kinetic equation that describe weakly interact
ing waves: J. Guioth\, F. Bouchet and G. L. Eyink\
, 2022\, J Stat Phys\, 189\, 20 \, arXiv:2203.1173
7.\n\nFor the large deviations associated with the
weak turbulence kinetic equation that describe we
akly interacting waves in heterogeneous versions:
Y. Onuki\, J. Guioth\, and F. Bouchet\, 2023\, arX
iv:2301.03257.
LOCATION:https://maths-cam-ac-uk.zoom.us/j/98016675669\, sc
reened in Center for Mathematical Sciences MR4
CONTACT:Camille Scalliet
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