Universality of thermodynamic relation with corrections in Einstein-Bel-Robinson gravity black holes*

Abstract The generalized thermodynamic extremum relation, as proposed by Goon and Penco, establishes a novel theoretical framework for studying spacetime thermodynamics. However, previous investigations generally assumed that the black hole state parameter is solely a first-order function of the perturbation parameter when exploring the Goon-Penco relation in diverse spacetime contexts. An analytic expression for the perturbation parameter as a function of the black hole entropy can be expressed by treating the black hole mass as constant. The present study addresses this limitation and provides insight into the universal Goon-Penco relation when multiple thermodynamic state parameters behave as higher order functions of the perturbation parameters. Notably, we have not only established a universal relational formula for multiple state variables, but more importantly, we have proposed an innovative conjecture that reveals the existence of a universal relation between displaced thermodynamic quantities in spacetime in the context of an arbitrary black hole. These theoretical breakthroughs are expected to enable new exploration directions for quantum gravity research.