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SUMMARY:Path large deviations for kinetic theories: beyond the Boltzmann\,
  the Landau\, and the Balescu—Lenard—Guernsey kinetic equations - Fred
 dy Bouchet (ENS - Lyon\, CNRS (Centre national de la recherche scientifiqu
 e))
DTSTART:20220425T133000Z
DTEND:20220425T143000Z
UID:TALK171827@talks.cam.ac.uk
DESCRIPTION:In many physical systems one seeks to describe effectively mes
 oscopic or macroscopic variables. Kinetic theories and kinetic equations a
 re examples where the average mesoscopic dynamics is obtained through very
  clear theoretical procedures and can possibly lead to mathematical proofs
 \, for instance the Landau or the Balescu&mdash\;Guernsey&mdash\;Lenard eq
 uations in plasma physics. A few works go beyond the average evolution and
  describe\, for instance\, Gaussian fluctuations. However\, for many physi
 cal systems\, rare events can be of importance\, and Gaussian fluctuations
  are not relevant. This is the case for instance if one wants to understan
 d the irreversibility paradox associated to the kinetic equations\, or to 
 understand the dynamics that leads to rare events with big impact.&nbsp\;\
 n&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\; The aim o
 f this presentation is to describe recent results where we derived explici
 tly the functional that describes the path large deviations for the empiri
 cal measure of dilute gases\, plasma and systems of particles with long ra
 nge interactions. The associated kinetic equations (the average evolution)
  are then either the Boltzmann\, the Landau or the Balescu--Lenard&mdash\;
 Guernsey equations. &nbsp\;After making the classic assumptions in theoret
 ical physics textbooks for deriving the kinetic equation\, our derivation 
 of the large deviation functional is exact.\nThese path large deviation pr
 inciples give a very nice and transparent new interpretation of the classi
 cal irreversibility paradox. This new explanation is fully compatible with
  the classical one\, but it gives a deeper insight.\nReferences:\nFor the 
 large deviations associated to the Boltzmann equation (dilute gazes)\, and
  a general introduction (published in J. Stat. Phys. in 2020): F. Bouchet\
 , 2020\, Is the Boltzmann equation reversible? A large deviation perspecti
 ve on the irreversibility paradox and the Boltzmann equation\, Journal of 
 Statistical Physics\, 181\, 515&ndash\;550\, https://link.springer.com/art
 icle/10.1007/s10955-020-02588-y\, https://arxiv.org/abs/2002.10398 \nFor t
 he large deviations associated to the Landau equation (plasma below the De
 bye length\, accepted for publication in J. Stat. Phys. in March 2021): O.
  Feliachi and F. Bouchet\, 2021\, Dynamical large deviations for plasma be
 low the Debye length and the Landau equation\, Journal of Statistical Phys
 ics\, 183\, 42\, https://link.springer.com/article/10.1007/s10955-021-0277
 1-9\, https://arxiv.org/abs/2101.04455.\nFor the large deviations associat
 ed with the Balescu&mdash\;Guernsey--Lenard equation (plasma and systems w
 ith long range interactions): O. Feliachi and F. Bouchet\, 2022\, Dynamica
 l Large Deviations for Homogeneous Systems with Long Range Interactions an
 d the Balescu&ndash\;Guernsey&ndash\;Lenard Equation\, Journal of Statisti
 cal Physics&nbsp\;186\, 22\, https://link.springer.com/article/10.1007/s10
 955-021-02854-7&nbsp\;and https://arxiv.org/abs/2105.05644\nJoint works wi
 th Ouassim Feliachi
LOCATION:Seminar Room 1\, Newton Institute
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