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Living systems are fundamentally irreversible, breaking detailed balance andestablishing an arrow of time. But how does the evident arrow of time for awhole system arise from the interactions among its multiple elements? We showthat the local evidence for the arrow of time, which is the entropy productionfor thermodynamic systems, can be decomposed. First, it can be split into twocomponents: an independent term reflecting the dynamics of individual elementsand an interaction term driven by the dependencies among elements. Adaptingtools from non--equilibrium physics, we further decompose the interaction terminto contributions from pairs of elements, triplets, and higher--order terms.We illustrate our methods on models of cellular sensing and logicalcomputations, as well as on patterns of neural activity in the retina as itresponds to visual inputs. We find that neural activity can define the arrow oftime even when the visual inputs do not, and that the dominant contribution tothis breaking of detailed balance comes from interactions among pairs ofneurons.

Emergence of local irreversibility in complex interacting systems