Fitting by hand

The bars are the data — a count that doesn't move. The line is the maximum-entropy model. Nudge the λ to bend it onto the bars, keeping an eye on the divergence below; or hit let it fit and watch the descent do the work for you.

The floor of surprise

The model's average surprise at the data is the cross-entropy. But there's a floor: the uncertainty the data themselves carry, their entropy. What sits above the floor is the divergence — the surprise that comes only from the model being wrong. Fit, and watch that part shrink.