Physical process first law and increase of horizon entropy for black   holes in Einstein-Gauss-Bonnet gravity
  We establish the physical process version of first law by studying small perturbations of a stationary black hole with regular bifurcation surface in Einstein-Gauss-Bonnet (EGB) gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies null energy condition. 
Ayan Chatterjee, Sudipta Sarkar
gr-qc hep-th