Physics Seminar
Date: Tuesday, 29 October 2024
Time: 11:45 AM - 12:45 PM
Venue: Seminar Hall
Contact Geometry and Thermodynamics
Aritra Ghosh
Indian Institute of Technology Bhubaneswar.
29-10-24

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Abstract

In this talk, I will discuss some aspects of contact geometry, with particular emphasis on thermodynamics. I will begin with a short introduction to contact geometry, briefly pointing out its relevance to dissipative mechanics. Thermodynamic phase spaces assume the structure of a contact manifold, with the points describing equilibrium states being restricted to certain submanifolds of this phase space. I will discuss gauge transformations and Legendre transforms, and shall also describe thermodynamic processes using contact Hamiltonian dynamics and the contact Hamilton-Jacobi equation, both of which are compatible with each other. Following this, I will describe the emer- gence of interacting thermodynamic systems from non-interacting ones via deformations induced by contact Hamiltonian vector fields. I will end with some discussion on the notion of metric structures (in the sense of Sasaki), putting emphasis on Hessian metrics and ensemble non-equivalence.