Physical Process First Law and the Entropy Change of Rindler Horizons

The physical process version of the first law can be obtained for bifurcate Killing horizons with certain assumptions. Especially, one has to restrict to the situations where the horizon evolution is quasi-stationary, under perturbations. We revisit the analysis of this assumption considering the horizon perturbations of Rindler horizon by a spherically symmetric object. We demonstrate that even if the quasi-stationary assumption holds, the change in entropy, in four space-time dimensions, diverges when considered between asymptotic cross-sections. However, these divergences do not appear in higher dimensions. We also analyze these features in the presence of a positive cosmological constant. In the process, we prescribe a recipe to establish the physical process first law in such ill-behaved scenarios.