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An eikonal equation approach to thermodynamics and the gradient flows in information geometry (2001.03437v3)
Published 10 Jan 2020 in cs.IT, cond-mat.stat-mech, math-ph, math.IT, and 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.
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