Thermodynamics and kinetics of state switching for the asymptotically flat black hole in a cavity

TL;DR

This paper explores the thermodynamics and kinetics of black hole state transitions within a cavity using free energy landscape formalism, revealing phase transitions and deriving kinetic timescales influenced by temperature and energy barriers.

Contribution

It introduces a free energy landscape approach to study black hole thermodynamics and kinetics, including phase diagrams and first passage time calculations.

Findings

Identifies Hawking-Page and Van der Waals phase transitions in black holes in a cavity.

Derives a recurrence relation for first passage time moments.

Shows kinetics depend on temperature and energy barrier height.

Abstract

We propose that the thermodynamics and the kinetics of state switching for the asymptotically flat black hole enclosed by a cavity can be studied in terms of the free energy landscape formalism. The generalized free energy for the black hole enclosed by a cavity in the canonical ensemble is derived by using the York's approach, where the temperature on the cavity and the charges inside the cavity are kept as the fixed parameters. By quantifying the corresponding free energy landscape, we obtain the phase diagrams for the black hole in cavity, which reveal a Hawking-Page type transition for the uncharged black hole and a Van der Waals type transition for the charged black hole. We further assume that the dynamics of black hole state switching is mutually determined by the gradient force and the stochastic force arising from the free energy landscape and the thermal noises respectively. We then derive a recurrence relation for the $n$-momentum of the first passage time distribution function, which enables the calculation of the kinetic times characterized by the mean first passage time and its relative fluctuation. Our analysis illustrates that the kinetics of black hole state switching is determined by the ensemble temperature and the barrier height on the free energy landscape.