A new measure of thermal micro-behavior for the AdS black hole * *The financial supports from National Natural Science Foundation of China (11947208, 11947301), China Postdoctoral Science Foundation (2020M673460), Major Basic Research Program of Natural Science of Shaanxi Province (2017KCT-12), Scientific Research Program Funded by Shaanxi Provincial Science and Technology Department (2019JQ-081) are gratefully acknowledged. This research is also particularly

Abstract

Inspired by the hypothesis of the black hole molecule, with the help of the Hawking temperature, entropy, and the thermodynamic curvature of black holes, we propose a new measure of the relation between the interaction and the thermal motion of molecules of the AdS black hole as a preliminary and coarse-grained description. The proposed measure introduces a dimensionless ratio to characterize this relation and shows that there is indeed competition between the interactions of black hole molecules and their thermal motion. For a charged AdS black hole, below the critical dimensionless pressure, there are three transitions between the interaction and thermal motion states. In contrast, above the critical dimensionless pressure, only one transition takes place. For the Schwarzschild-AdS and five-dimensional Gauss-Bonnet AdS black holes, a transition always occurs between the interaction and thermal motion states.