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We establish the physical process version of first law by studying smallperturbations of a stationary black hole with regular bifurcation surface inEinstein-Gauss-Bonnet (EGB) gravity. Our result shows that when the stationaryblack hole is perturbed by a matter stress energy tensor and finally settlesdown to a new stationary state, the Wald entropy increases as long as thematter satisfies null energy condition.

Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity