  In this study, we investigate the dynamics and frame-by-frame phase
transition of the first order in black hole thermodynamics. For our analysis,
we will utilize the Kramers escape rate. Our focus is on charged anti-de Sitter
(AdS) black holes influenced by Kaniadakis and Barrow statistics. The selection
of these black holes aims to examine the effects of entropy variation on the
dynamics of phase transition and to demonstrate that the Kramers escape rate,
as an efficient tool, can effectively represent the dynamic transition from a
small to a large black hole within the domain of first-order phase transitions.
It is noteworthy that while the transition from small to large black holes
should ostensibly dominate the entire process, our results indicate that the
escape rate undergoes changes as it passes through the midpoint of the phase
transition, leading to a reverse escape phenomenon. The findings suggest that
the dynamic phase transition in charged AdS black holes affected by entropy
change bears a significant resemblance to the outcomes of models influenced by
Bekenstein-Hawking entropy\cite{23}. This similarity in results could serve as
an additional motivation to further explore the potential capabilities of
Kaniadakis and Barrow statistics in related cosmological fields. These
capabilities could enhance our understanding of other cosmological properties
