An eikonal equation approach to thermodynamics and the gradient flows in information geometry. (English) Zbl 07458616
Summary: 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.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
eikonal equation; gradient-flow equations; information geometry; Hamilton-Jacobi dynamics; thermodynamics; vielbeinReferences:
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