Off-shell Thermodynamics and Kinetics of Holographic CFTs Dual to Charged AdS Black Holes

Abstract

We study the thermodynamics and phase structure of holographic conformal field theories dual to spherically symmetric charged AdS black holes using an off-shell free energy. We consider three ensembles of the dual CFT with fixed: $(\tilde Q,{\cal V},C)$, $(\tilde Φ,{\cal V},C)$, and $(\tilde Q,{\cal V},μ)$ and present their corresponding phase diagrams. For the fixed $(\tilde Q,{\cal V},C)$ and $(\tilde Φ,{\cal V},C)$ ensembles, we study the transitions between competing states using a stochastic description on the various phases given by off-shell free energy. This is described by an ensemble dependent Fokker-Planck equation, allowing us to compute the first-passage-time distribution, including the mean first passage time and its fluctuations over a range of temperatures. We also examine how the phase structure and the associated kinetics depend on the electric charge $\tilde Q$ and the central charge $C$.