Notes on sums over horizons

For a large class of black holes, we show that the sum of thermodynamic quantities over all the horizons is determined by the asymptotic data at infinity. For the Kerr-Newman metric, this proves a recent numerical observation by Hristov. We propose a new method to compute the sum of the entropies using a generalized Smarr formula. The higher-curvature corrections in Gauss-Bonnet gravity are discussed.