Particle absorption by black holes and the generalized second law of thermodynamics

The change in entropy, Delta S, associated with the quasi- static absorption of a particle of energy epsilon by a Schwarzschild black hole (ScBH) is approximately (epsilon/T) - s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. Motivated by the statistical interpretation of entropy, it is proposed here that the absorption should be suppressed, but not forbidden, when Delta S < 0, which requires the absorption cross section to be sensitive to Delta S. A purely thermodynamic formulation of the probability for the absorption is obtained from the standard relationship between microstates and entropy. If Delta S >> 1 and s << epsilon/T, then the probability for the particle not to be absorbed is approximately exp[-epsilon/T], which is identical to the probability for quantum mechanical reflection by the horizon of an ScBH. The manifestation of quantum behaviours in the new probability function may intimate a fundamental physical unity between thermodynamics and quantum mechanics.