Black hole, as an outstanding prediction of Einstein gravity, is one of the most fascinating and mysterious compact subjects. This prediction is confirmed by observational data (1; 2). In addition, one of the remarkable achievements of theoretical physics is related to the discovery of a profound connection between the laws of black hole mechanics with the corresponding laws of ordinary thermodynamic systems (3; 5; 4). On the other hand, the study of black hole thermodynamics in an anti-de Sitter (AdS) space provides remarkable holographic inputs in our efforts to understand the quantum nature of gravity (6; 7; 8).In the context of AdS spacetimes, Hawking-Page phase transition(9) has already shown the existence of novel physics connecting black holes and finite temperature confirmal field theories(8), together with their interesting phase transition structure (10; 11). More recently, exciting developments are taking place due to the emergence of concrete relation between AdS black holes and van der Waals liquid-gas system (