  A major challenge in the study of active matter lies in quantitative
characterization of phases and transitions between them. We show how the
entropy of a collection of active objects can be used to classify regimes and
spatial patterns in their collective behavior. Specifically, we estimate the
contributions to the total entropy from correlations between the degrees of
freedom of position and orientation. This analysis pin-points the flocking
transition in the Vicsek model while clarifying the physical mechanism behind
the transition. When applied to experiments on swarming Bacillus subtilis with
different cell aspect ratios and overall bacterial area fractions, the entropy
analysis reveals a rich phase diagram with transitions between qualitatively
different swarm statistics. We discuss physical and biological implications of
these findings.
