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

英文摘要：

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.