  Living systems are fundamentally irreversible, breaking detailed balance and
establishing an arrow of time. But how does the evident arrow of time for a
whole system arise from the interactions among its multiple elements? We show
that the local evidence for the arrow of time, which is the entropy production
for thermodynamic systems, can be decomposed. First, it can be split into two
components: an independent term reflecting the dynamics of individual elements
and an interaction term driven by the dependencies among elements. Adapting
tools from non--equilibrium physics, we further decompose the interaction term
into contributions from pairs of elements, triplets, and higher--order terms.
We illustrate our methods on models of cellular sensing and logical
computations, as well as on patterns of neural activity in the retina as it
responds to visual inputs. We find that neural activity can define the arrow of
time even when the visual inputs do not, and that the dominant contribution to
this breaking of detailed balance comes from interactions among pairs of
neurons.
