Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape

We study the phase transition and the kinetics of the four dimensional charged AdS black hole in GB gravity based on the free energy landscape. Below the critical temperature, the free energy landscape topography has the shape of double basins with each representing one stable/unstable black hole phase. The thermodynamic small/large black hole phase transition is determined by the equal depths of the basins. We also demonstrate the underlying kinetics of the phase transition by studying the time evolution of the probability distribution of the state in the ensemble as well as the MFPT and the kinetic fluctuation of the state switching process caused by the thermal fluctuations. The final distribution is determined by the Boltzmann law and the MFPT and its fluctuation are closely related to the free energy landscape topography through barrier heights and ensemble temperature. Furthermore, we provide a complete description of the kinetics of phase transition with different physical parameters. The free energy is the result of the delicate balance and competition between the two relatively large numbers, the energy and entropy multiplied by temperature. Low energy and low entropy can give rise to a stable thermodynamic state in terms of free energy minimum (energy/mass preferred) while the high energy and high entropy can also give rise to a stable state in terms of free energy minimum. When the GB coupling constant increases, or the electric charge (potential) increases, or the pressure (absolute value of cosmological constant) decreases, it is easier for the small black hole state to escape to the large black hole state. Meanwhile, the inverse process becomes harder, i.e. the small (large) black hole state becomes less (more) stable.