Kinetics of a phase transition for a Kerr-AdS black hole on the free-energy landscape

Abstract

By treating the black hole event horizon as a stochastic thermal fluctuating variable for small-large black hole phase transition, we investigate the dynamical process of phase transition for the Kerr AdS black holes on free energy landscape. We find that the extremal points of the off-shell Gibbs free energy correspond to physical black holes. For small-large black hole phase transition, the off-shell Gibbs free energy exhibits a double well behavior with the same depth. Contrary to previous research for the dynamics of phase transition for the Kerr-Newman AdS family black holes on free energy landscape, we find that there is a lower bound for the order parameter and the lower bound corresponds to extremal black holes. In particular, the off-shell Gibbs free energy is zero instead of divergent as previous work suggested for vanishing black hole horizon radius, which corresponds to the Gibbs free energy of thermal AdS space. The investigation for the evolution of the probability distribution for the phase transition indicates that the initial stable small (large) black hole tends to switch to stable large (small) black hole. Increasing the temperature along the coexistence curve, the switching process becomes faster and the probability distribution reaches the final stationary Boltzmann distribution at a shorter time. The distribution of the first passage time indicates the time scale of the small-large black hole phase transition, and the peak of the distribution becomes sharper and shifts to the left with the increase of temperature along the coexistence curve. This suggests that a considerable first passage process occurs at a shorter time for higher temperature.

Free energy landscape and kinetics of phase transition in two coupled SYK models

“…In the formalism of the free energy landscape [32][33][34][35], the Gibbs free energy is defined as the continuous function of the order parameter or reaction coordinate of the system. The order parameter or reaction coordinate may be considered as the coarse-grained description which captures the essential characteristics and the microscopic degree of freedom of the system [38][39][40][41][42][43][44][45][46][47][48][49].…”

“…The probability distribution of the states (on-shell solutions as well as the off-shell solutions on the free energy landscape) are denoted by ρ(σ). The stochastic kinetics of states under the thermal fluctuation can be described by the probabilistic Fokker-Planck equation, which on the free energy landscape is explicitly given by [38][39][40][41][42][43][44][45][46][47][48][49]…”

“…Furthermore, we propose the kinetics of the phase transition between the wormhole and two black hole can be investigated by using the stochastic dynamics on the free energy landscape. We assume the phase transition between the wormhole and two black hole is a stochastic process under the thermal fluctuations and study the probabilistic Fokker-Planck equation which describes the kinetics of the phase transition [38][39][40][41][42][43][44][45][46][47][48][49]. By calculating the kinetics time and its fluctuation, we reveal the underlying thermodynamics and kinetics of the phase transition between the wormhole and two black hole.…”

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

“…The third force represents the stochastic force that comes from the microscopic degrees of freedom of the effective heat bath. Under these assumptions, the Langevin equation or the equivalent Fokker-Planck equation are employed to calculate the kinetic time and reveal the dynamical properties of the black hole phase transitions [35][36][37][38][39][40][41][42][43][44][45][46][47]. In [34], the possibility of probing the black hole microstructure from the kinetic turnover of the small/large RNAdS black hole phase transition was discussed.…”

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

“…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].…”