  This paper presents the first numerical study of black hole thermodynamics in
Causal Set Theory, focusing on the entropy of a Schwarzschild black hole as
embodied in the distribution of proposed horizon molecules. To simulate causal
sets we created a highly parallelized computational framework in \texttt{C++}
which allowed for the generation of causal sets with over a million points, the
largest causal sets in a non-conformally flat spacetime to date. Our results
confirm that the horizon molecules model is consistent with the
Bekenstein-Hawking formula up to a dimensionless constant that can be
interpreted as the fundamental discreteness scale in the order of a Planck
length. Furthermore, the molecules are found to straddle the horizon of the
black hole to within a few Planck lengths, indicating that entropy lives on the
surface of the black hole. Finally, possible implications for the information
paradox are drawn. In particular, we show how the horizon molecules model could
yield a finite black hole temperature cut-off or even prevent full black hole
evaporation.
