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We study the phase transition and the kinetics of the four dimensionalcharged AdS black hole in GB gravity based on the free energy landscape. Belowthe critical temperature, the free energy landscape topography has the shape ofdouble basins with each representing one stable/unstable black hole phase. Thethermodynamic small/large black hole phase transition is determined by theequal depths of the basins. We also demonstrate the underlying kinetics of thephase transition by studying the time evolution of the probability distributionof the state in the ensemble as well as the MFPT and the kinetic fluctuation ofthe state switching process caused by the thermal fluctuations. The finaldistribution is determined by the Boltzmann law and the MFPT and itsfluctuation are closely related to the free energy landscape topography throughbarrier heights and ensemble temperature. Furthermore, we provide a completedescription of the kinetics of phase transition with different physicalparameters. The free energy is the result of the delicate balance andcompetition between the two relatively large numbers, the energy and entropymultiplied by temperature. Low energy and low entropy can give rise to a stablethermodynamic 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 interms of free energy minimum. When the GB coupling constant increases, or theelectric charge (potential) increases, or the pressure (absolute value ofcosmological constant) decreases, it is easier for the small black hole stateto escape to the large black hole state. Meanwhile, the inverse process becomesharder, i.e. the small (large) black hole state becomes less (more) stable.

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