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

Tatsuaki Wada, Antonio M. Scarfone and Hiroshi Matsuzoe

Physica A: Statistical Mechanics and its Applications, 2021, vol. 570, issue C

Abstract: We can incorporate a “time” evolution into thermodynamics as a Hamilton–Jacobi dynamics. A set of the equations of state 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.

Keywords: Eikonal equation; Gradient-flow equations; Information geometry; Hamilton–Jacobi dynamics; Thermodynamics; Vielbein (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:570:y:2021:i:c:s0378437121000923

DOI: 10.1016/j.physa.2021.125820

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