Ideal Gas Limit and Equipartition Theorem for AdS Black Holes

In the framework of black hole chemistry, we present an equipartition theorem for four-dimensional AdS black holes with spherically symmetric and static horizons in Einstein gravity. It is found that at high temperatures, the total enthalpy of the spacetime is equally shared among the putative microstructures of the black hole horizon with each degree of freedom contributing \(k_B T_\textrm{H}\) . This strengthens the analogy between the thermodynamics of gases and that of black holes. Finally, we demonstrate the consistency of our result from a holographic point of view.