RPST-inspired formalism for black holes in flat spacetime

In this work, we propose a formalism for the thermodynamics of flat black holes in Renyi statistics, inspired by the Restricted Phase Space Thermodynamics (RPST) framework. Our construction is motivated by the observed similarities in the thermodynamic behavior of flat black holes within the Rényi entropy framework and that of AdS black holes described by the Bekenstein entropy regime. We introduce a deformation parameter λ to replace the central charge C . This RPST-inspired formalism incorporates λ and its conjugate variable, the response potential ζ , as a new pair of thermodynamic variables, analogous to the central charge C and chemical potential μ in the AdS case. To illustrate the applicability of this formalism, we analyze two examples: the Reissner-Nordström (RN) flat black hole and the Kerr black hole.