Entropy correction and phase transition of n-dimensional charged dilaton dS black holes

Abstract

Abstract The manifest disparity in Hawking radiation temperatures between black hole and cosmological horizons in de Sitter (dS) spacetime reveals a non-equilibrium thermal configuration, inherently violating thermodynamic stability criteria. This asymmetry poses significant challenges to the systematic analysis of dS thermodynamics. In this study, we construct a thermodynamic framework for dS spacetime under the condition that the system’s thermodynamic quantities adhere to the first law of thermodynamics, while enforcing thermal equilibrium between horizons through radiation temperature-equivalent conditions. Our ansatz postulates that spacetime entropy constitutes both horizon entropy contributions with a supplementary correction term. Through variational analysis constrained by equilibrium thermodynamics, we derive and solve thermodynamic constraints to obtain corrected entropy relations that explicitly resolve the two-horizon entropy puzzle for n-dimensional charged dilaton-dS black holes. Utilizing these corrected entropy relations, we renormalize associated thermodynamic quantities, thereby establishing self-consistent extended thermodynamics. Numerical solutions of the Gibbs criteria reveal parameter-dependent critical points, where heat capacity is diverging signal possible second-order phase transitions. The system manifests phase transition phenomena, structurally homologous to liquid–gas transition in conventional thermodynamic systems. We proved that the system satisfies the conditions for equilibrium stability, allowing equilibrium phase transitions to occur near critical points.