The agenda of next meetings of Krasil'shchik's seminar on geometry of
differential equations at the Independent University of Moscow.

On 11 February the seminar meets offline in room 303 of the Independent
University of Moscow, on 19:20 MSK, simultaneously, there will be
broadcast via Zoom.

Speaker: Valentin Lychagin
Title: On the management of thermodynamic processes
Language: English
Zoom:

Abstract:

At the beginning of the talk, three geometric approaches to
thermodynamics will be discussed.

The first approach is the Gibbs energy approach, which will be
reformulated in terms of contact geometry and where the description of
substances (the so-called equations of state) is given in terms of
Legendre submanifolds in thermodynamic contact phase spaces, and
thermodynamic processes, as well as controls, will be given by contact
vector fields.

The second approach is based on information geometry and follows the
principle 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 submanifolds.

The third approach is based on the geometry of jet spaces (or the
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 transitions.

Thermodynamic 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.

The set of controls forms a Lie algebra, in which the Lie algebra of
symmetries is a Lie subalgebra.

We will present equations that depend on the equations of state of the
medium and allow us to find control processes, as well as illustrate
their application in the case of adiabatic processes.

If time permits, phase transitions of the first, second and higher
orders will be considered, both in thermodynamic processes and in
controls, as well as their connection with Arnold's theory on the
singularities of projections of Lagrangian manifolds.


The seminar meets on Wednesday evenings at 19:20 MSK in room 303
and in Zoom, Meeting ID: 88 17 12 1842
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FROM 202.120.11.*