On some phase equilibrium features of charged black holes in flat spacetime via Rényi statistics

Motivated by the nonextensive nature of entropy in the gravitational context and the Gauge/Gravity duality, black hole thermodynamics has been attracting intense emphasis in the literature. Along the present work, we investigate some features of the phase structure and critical phenomena of the 4-dimensional charged black holes in asymptotically flat spacetime within the formalism of Rényi statistics. First, we explore the extended phase space via the Rényi statistics approach. Concretely, based on the modified version of the Smarr formula, we recall the equal-area law to remove the oscillatory non-physical region in the \(P_R-V\) and \(T_R-S_R\) planes. Then, the coexistence curves are determined, as well as the latent heat of phase change. Moreover, we prove that the critical exponent describing the behavior of the order parameter near the critical point is \(\frac{1}{2}\), which is consistent with Landau’s theory of continuous phase transition. Lastly, we apply the Hamiltonian approach to Rényi thermodynamics which provides a new and solid mathematical basis for the extension of phase space and puts more insight into an expected and profound possible connection between the nonextensivity Rényi parameter \(\lambda \) and the cosmological constant \( \Lambda \).