Dynamic properties of thermodynamic phase transition for five-dimensional neutral Gauss-Bonnet AdS black hole on free energy landscape

TL;DR

This paper explores the dynamic behavior of phase transitions between small and large black holes in five-dimensional Gauss-Bonnet AdS spacetime, revealing how thermal fluctuations influence black hole state transitions and their probabilities.

Contribution

It provides a detailed analysis of the free energy landscape and the probability evolution of black hole phase transitions, incorporating thermal fluctuations and first passage time calculations.

Findings

Black hole solutions correspond to extremal points on the free energy landscape.

Thermal fluctuations enable transitions between small and large black hole states.

Higher temperatures accelerate the transition probabilities and reduce first passage times.

Abstract

Understanding the dynamic process of the thermodynamic phase transition can provide the deep insight into the black hole microscopic properties and structures. We in this paper study the dynamic properties of the stable small-large black hole phase transition for the five-dimensional neutral Gauss-Bonnet AdS black hole. Firstly, by using the first law of black holes, we prove that the extremal points of the free energy on the landscape denote the real black hole solutions satisfying the field equations. The local maximal and minimal points correspond to local unstable and stable black hole states, respectively. Especially, on the free energy landscape, the wells of the coexistence small and large black holes have the same depth. Then we investigate the probability evolution governed by the Fokker-Planck equation. Due to the thermal fluctuation, we find that the small (large) black hole state can transit to the large (small) black hole state. Furthermore, the first passage time is calculated. For each temperature, a single peak is presented, which suggests that there is a considerable fraction of the first passage events taking place at short time. And the higher the temperature is, the faster decrease of the probability is. These results will uncover some intriguing dynamic properties of the stable small-large black hole phase transition in modified gravity.