  The phase transition has always been a major focus in the study of black hole
thermodynamics. This study employs the Kramer escape rate from stochastic
processes to investigate the first-order phase transition strength between the
large and small black hole states. The results indicate that the phase
transition of the third-order Lovelock black holes exhibits significant
asymmetric characteristics in diverse dimensions both in the hyperbolic and
spherical topology, with an overall trend of the transition from large black
holes to small black holes. Especially for the spherical topology, when the
dimension is higher than seven, there exists a certain temperature beyond which
a dynamic equilibrium is established for the phase transition. This study
provides valuable insights into the first-order phase transition rate of black
holes and enriches the understanding of black hole phase transitions.
