An eikonal equation approach to thermodynamics and the gradient flows in information geometry
Information Theory
2021-08-16 v3 Statistical Mechanics
Mathematical Physics
math.IT
math.MP
Abstract
We can incorporate a "time" evolution into thermodynamics as a Hamilton-Jacobi dynamics. A set of the equations of states in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton-Jacobi equation. We relate the Hamilton-Jacobi dynamics of a simple thermodynamic system to the gradient flows in information geometry.
Cite
@article{arxiv.2001.03437,
title = {An eikonal equation approach to thermodynamics and the gradient flows in information geometry},
author = {Tatsuaki Wada and Antonio M. Scarfone and Hiroshi Matsuzoe},
journal= {arXiv preprint arXiv:2001.03437},
year = {2021}
}
Comments
Submitted to Physica A