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

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.

Submitted to Physica A

References in corpus (3)

• A Hamilton-Jacobi Formalism for Thermodynamics
• Contact geometry and thermodynamics of black holes in AdS spacetimes
• The Hamilton-Jacobi Equation: an intuitive approach

Cited by in corpus (5)

• On the Kaniadakis distributions applied in statistical physics and natural sciences
• A Hamiltonian approach to the gradient-flow equations in information geometry
• Mechanics of geodesics in Information geometry and Black Hole Thermodynamics
• Hamilton-Jacobi approach to thermodynamic transformations
• Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning