  We show that the evidence for a local arrow of time, which is equivalent to
the entropy production in thermodynamic systems, can be decomposed. In a system
with many degrees of freedom, there is a term that arises from the irreversible
dynamics of the individual variables, and then a series of non--negative terms
contributed by correlations among pairs, triplets, and higher--order
combinations of variables. We illustrate this decomposition on simple models of
noisy logical computations, and then apply it to the analysis of patterns of
neural activity in the retina as it responds to complex dynamic visual scenes.
We find that neural activity breaks detailed balance even when the visual
inputs do not, and that this irreversibility arises primarily from interactions
between pairs of neurons.
