Thermodynamics of asymptotically de Sitter black hole in dRGT massive gravity from Rényi entropy

The thermodynamic properties of the de Rham-Gabadadze-Tolley (dRGT) black hole in asymptotically Sitter (dS) spacetime are investigated by using R\'enyi entropy. It has been found that with dS described standard Gibbs-Boltzmann statistics cannot be thermodynamically stable. Moreover, there generically exist two horizons corresponding to systems different temperatures, leading a nonequilibrium state. Therefore, order obtain stable dRGT hole, we use alternative analyze thermodynamics both separated system approach and effective approach. Interestingly, it is possible concurrently positive pressure volume for while not Schwarzschild-de (Sch-dS) hole. Furthermore, bounds on nonextensive parameter which being determined. In addition, key differences between approaches, e.g., temperature profiles types Hawking-Page phase transition pointed out.