Fig. S1.

(A) Mutual information plotted for the delta distribution $\rho \left(\mathrm{\Delta }\right)=\delta \left(\mathrm{\Delta }-\mu \right)$ for various (log-spaced) $\beta \mu$. I displays a characteristic rise with $\log \left(N\right)$, maximum, and then a decay at large N. (B) The capacity is plotted for $\rho \left(\mathrm{\Delta }\right)=\delta \left(\mathrm{\Delta }-\mu \right)$. As $\beta \mu$ gets large, capacity is linear. (C) Mutual information plotted for the exponential distribution $\rho \left(\mathrm{\Delta }\right)=\left(1/\mu \right)e^{-\mathrm{\Delta }/\mu }$ for various (log-spaced) $\beta \mu$. I displays a characteristic rise with $\log \left(N\right)$ and then plateaus at its maximum. (D) The capacity as a function of $\beta \mu$ for the exponential distribution. As $\beta \mu$ gets large, the capacity goes as $\log \left(\beta \mu \right)$ (the x axis is log scale).