The entropy-reduction hypothesis claims that the cognitive processing difficulty on a word in sentence context is determined by the word's effect on the uncertainty about the sentence. Here, this hypothesis is tested more thoroughly than has been done before, using a recurrent neural network for estimating entropy and self-paced reading for obtaining measures of cognitive processing load. Results show a positive relation between reading time on a word and the reduction in entropy due to processing that word, supporting the entropy-reduction hypothesis. Although this effect is independent from the effect of word surprisal, we find no evidence that these two measures correspond to cognitively distinct processes.