Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape

Abstract

We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.

The kinetics and its turnover of Hawking-Page phase transition under the black hole evaporation

“…The kinetic process of the phase transition under the thermal fluctuations which is a stochastic process can be properly described by the stochastic Langevin equation or equivalently by the corresponding Fokker-Planck equation [24]. Based on this proposal, the kinetic time characterized by the mean first passage time can be calculated, which is shown to be closely related to the barrier height on the free energy landscape [25][26][27][28].…”

Dynamic Property of Phase Transition for Non-Linear Charged Anti-de Sitter black holes

“…Recently, authors in Refs. [54] proposed that Gibbs free energy landscape should also correspond to the thermal dynamic phase transition of a black hole. In this section, we will investigate the thermal dynamic phase transition of the EPYM AdS black hole from the view of Gibbs free energy landscape.…”

“…In this approach, the phase transition is due to the thermal fluctuation and G L is regarded an function of black hole horizon which is the order parameter of phase transition. Subsequently, this method was applied to the HP phase transition in Einstein gravity [53] and in massive gravity [54] and the large/small black hole phase transition in Gauss-Bonnet gravity [55], in Einstein gravity [56] minimally coupled to nonlinear electrodynamics [57], and in dilaton gravity [58].…”

Kinetics of Hawking-Page phase transition with the non-Markovian effects

“…All the spacetime states compose a canonical ensemble, and the probability of the system in a specific state is then determined by the Boltzmann law p ∼ e −βG , where β is the inverse temperature of the canonical ensemble and G is the generalized free energy. Under the thermal fluctuations, the order parameter changes continuously, and the generalized free energy as the function of the order parameter has the shape of single well or double well depending on the ensemble temperature [32][33][34]. This is the free energy landscape formalism of black hole phase transition.…”

“…A recent effort on this aspect is to employ the free energy landscape formalism [28][29][30][31] to study the dynamical processes of the Hawking-Page phase transition [32] as well as the small/large RNAdS black hole phase transition [33,34]. An essential concept is the order parameter of the macroscopic black hole state that represents the microscopic degrees of freedom of the black hole state.…”