There is one paragraph that says: " Our starting assumption is directly motivated by Bekenstein's original thought experiment from which he obtained is famous entropy formula. He considered a particle with mass m attached to a ctitious "string" that is lowered towards a black hole. Just before the horizon the particle is dropped in. Due to the innite redshift the mass increase of the black hole can be made arbitrarily small, classically. If one would take a thermal gas of particles, this fact would lead to problems with the second law of thermodynamics. Bekenstein solved this by arguing that when a particle is one Compton wavelength from the horizon, it is considered to be part of the black hole. Therefore, it increases the mass and horizon area by a small amount, which he identied with one bit of information. This lead him to his area law for the black hole entropy." I don't quite understand what he meant when he gave the thermal gas example. How does it lead to problems with the second law of thermodynamics? Also how exactly does a particle being a Compton of wavelength away from the horizon (so as becoming part of the black hole) solve the problem?