Universal upper bound on the entropy-to-energy ratio for bounded systems

@article{Bekenstein1981UniversalUB,
title={Universal upper bound on the entropy-to-energy ratio for bounded systems},
author={J. Bekenstein},
journal={Physical Review D},
year={1981},
volume={23},
pages={287-298}
}

We present evidence for the existence of a universal upper bound of magnitude $\frac{2\ensuremath{\pi}R}{\ensuremath{\hbar}c}$ to the entropy-to-energy ratio $\frac{S}{E}$ of an arbitrary system of effective radius $R$. For systems with negligible self-gravity, the bound follows from application of the second law of thermodynamics to a gedanken experiment involving a black hole. Direct statistical arguments are also discussed. A microcanonical approach of Gibbons illustrates for simple systemsâ€¦Â Expand