Phase transitions in 4D Gauss–Bonnet–de Sitter black holes

We investigate thermodynamic aspects of black holes in the recently formulated four dimensional Gauss-Bonnet theory gravity, focusing on its asymptotically de Sitter ($\Lambda>0$) solutions. take a Euclidean path integral approach, where data is fixed at finite radius `cavity' outside hole to achieve equilibrium presence cosmological horizon. Working extended phase space constant treated as pressure, we study structure both uncharged and charged solutions, uncovering wealth phenomena. In case, are found undergo either standard Hawking-Page-like transition empty or small-large (akin those seen AdS pure Einstein gravity) depending pressure. also find triple point radiation, small, large phases coexist, zeroth-order within narrow range coupling parameter. Reentrant transitions between radiation small exist inside certain parameter range. Similar phenomena with charge playing role analogous determining structure.