Why is the black hole entropy (almost) linear in the horizon area?

We show that essentially pure classical thermodynamics is sufficient to determine Bekenstein’s formula for the black hole’s entropy, $S=\eta A.\mathrm{}$ We base our reasoning on the minimal assumption that since blackbody radiation is describable by classical thermodynamics, so is the complete black-hole–Hawking radiation system. Furthermore, we argue that any nonlinear correction to the black hole entropy must be quantum mechanical in nature. The proportionality coefficient, $\eta {=1/4l}_P^2,$ must be calculated within a semiclassical or full-fledged quantum mechanical framework.