  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.
