Observing dynamic oscillatory behavior of triple points among black hole thermodynamic phase transitions

Abstract

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.

Free energy landscape and kinetics of phase transition in two coupled SYK models and the corresponding wormhole-two black hole switching

“…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.…”

Thermodynamic phase transition of Euler-Heisenberg-AdS black hole on free energy landscape

“…By numerically calculating the Fokker-Planck equation, Li, Zhang and Wang studied the van der waals type phase transition in RN-AdS black holes from the viewpoint of free energy landscape, and obtained the probability distribution of states and time distribution of first passage kinetic process of black hole state switching [29]. These results revealed some interesting dynamic properties of the phase transition, therefore the dynamic process of the phase transition on the free energy landscape has been attracted significant attention recently [30,31].…”

Path integral and instantons for the process and phase transition rate of the RNAdS black hole

“…By viewing the cosmological constant as thermodynamic pressure in the AdS space, the analogues of charged-AdS black holes and the Van der Waals fluids have been explored [7][8][9]. The behaviors of the black hole thermodynamics at the triple point phase transition have also been investigated [10]. All of these studies provide us a more profound understanding to black hole thermodynamics.…”