Abstract:

We consider the concept of thermodynamic length within the framework of thermodynamic information geometry. Our goal is to show how the geodesic distance, defined on the space of equilibrium states, can be used to study the properties of finite-time processes in the system. It can also be used to detect critical and phase transition points in the system without referring to any ordering parameters. Because of its geometric nature thermodynamic length can be applied to various systems. As an example, we consider the warped anti-de Sitter black hole solution in 3 dimensions. It is holographically dual to a two-dimensional warped conformal field theory with two central charges. We calculate the thermodynamic length with respect to two different measures on the state manifold and show which process is allowed. As a consequence of knowing the thermodynamic length we can find the relaxation time and the speed of the process.