Phase Transition Dynamics of Black Holes Influenced by Kaniadakis and Barrow Statistics

TL;DR

This paper explores the phase transition dynamics of charged AdS black holes influenced by Kaniadakis and Barrow statistics, revealing a reverse escape phenomenon and highlighting the effectiveness of the Kramers escape rate in modeling these transitions.

Contribution

It introduces the use of Kaniadakis and Barrow entropy models to analyze black hole phase transitions and demonstrates the Kramers escape rate's effectiveness in capturing dynamic transition behaviors.

Findings

Identification of a reverse escape phenomenon during phase transition

Similarity of results to Bekenstein-Hawking entropy models

Potential implications for cosmological studies

Abstract

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