Topology of the landscape and dominant kinetic path for the thermodynamic phase transition of the charged Gauss-Bonnet-AdS black holes

We study the generalized free energy of five dimensional charged Gauss-Bonnet anti--de Sitter (AdS) black holes in grand canonical ensemble by treating hole radius and charge as order parameters. On two landscape, lowest points basins represent local stable saddle point represents unstable hole. show that is topological defect gradient field landscape. The stability determined topography landscape terms basin depths barrier height between not topology field. In addition, we stochastic dynamics phase transition obtain dominant kinetic path for on Unlike one small large state does necessarily pass through intermediate state. Furthermore, inhomogeneity diffusions can lead to switching from coupled cooperative process decoupled sequential process, giving different mechanisms.