An eikonal equation approach to thermodynamics and the gradient flows in information geometry

Tatsuaki Wada; Antonio M. Scarfone; Hiroshi Matsuzoe

doi:10.1016/j.physa.2021.125820

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arXiv · 2001.03437

An eikonal equation approach to thermodynamics and the gradient flows in information geometry

Tatsuaki Wada·Antonio M. Scarfone·Hiroshi Matsuzoe

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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.

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Tatsuaki Wada, Antonio M. Scarfone, Hiroshi Matsuzoe. 2020-10-21. An eikonal equation approach to thermodynamics and the gradient flows in information geometry. https://doi.org/10.1016/j.physa.2021.125820

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