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SUMMARY:Valentin Lychagin
DTSTART:20260211T162000Z
DTEND:20260211T180000Z
DTSTAMP:20260423T023020Z
UID:GDEq/150
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/150/">O
 n the management of thermodynamic processes</a>\nby Valentin Lychagin as p
 art of Geometry of differential equations seminar\n\nLecture held in room 
 303 of the Independent University of Moscow.\n\nAbstract\nAt the beginning
  of the talk\, three geometric approaches to thermodynamics will be discus
 sed.\n\nThe first approach is the Gibbs energy approach\, which will be re
 formulated in terms of contact geometry and where the description of subst
 ances (the so-called equations of state) is given in terms of Legendre sub
 manifolds in thermodynamic contact phase spaces\, and thermodynamic proces
 ses\, as well as controls\, will be given by contact vector fields.\n\nThe
  second approach is based on information geometry and follows the principl
 e of maximum entropy\, also known as the principle of minimum information 
 gain or Occam's razor. Both of these approaches lead us to the same model 
 of thermodynamics\, but they also introduce important new concepts\, such 
 as the Gibbs-Duhem principle and Riemannian structures on Legendre submani
 folds.\n\nThe third approach is based on the geometry of jet spaces (or th
 e geometry of differential equations)\, and it provides a more convenient 
 apparatus for the practical description and calculation of both equations 
 of state and thermodynamic processes\, taking into account phase transitio
 ns.\n\nThermodynamic process control will be understood as a thermodynamic
  process that does not destroy the process in question\, but allows it to 
 be accelerated or slowed down. \n\nThe set of controls forms a Lie algebr
 a\, in which the Lie algebra of symmetries is a Lie subalgebra. \n\nWe wi
 ll present equations that depend on the equations of state of the medium a
 nd allow us to find control processes\, as well as illustrate their applic
 ation in the case of adiabatic processes.\n\nIf time permits\, phase trans
 itions of the first\, second and higher orders will be considered\, both i
 n thermodynamic processes and in controls\, as well as their connection wi
 th Arnold's theory on the singularities of projections of Lagrangian manif
 olds.\n\nPlease download the formula file <a href="https://gdeq.org/files/
 td.pdf" title="td.pdf">td.pdf</a> and keep it handy during the talk so tha
 t the speaker can refer to it.\n
LOCATION:https://researchseminars.org/talk/GDEq/150/
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