Black hole motion in entropic reformulation of general relativity

We consider a system of black holes – a simplest substitute of a system of point particles in the mechanics of general relativity – and try to describe their motion with the help of entropic action: a sum of the areas of black hole horizons. We demonstrate that such description is indeed consistent with the Newton's laws of motion and gravity, modulo numerical coefficients, which coincide but seem different from unity. Since a large part of the modern discussion of entropic reformulation of general relativity is actually based on dimensional considerations, for making a next step it is crucially important to modify the argument, so that these dimensionless parameters acquire correct values.