  A defining feature of living matter is the ability to harness energy to
self-organize multiscale structures whose functions are facilitated by
irreversible nonequilibrium dynamics. While progress has been made in
elucidating the underlying principles, what remains unclear is the role that
thermodynamics plays in shaping these structures and their ensuing functions.
Here, we unravel how a fundamental thermodynamic connection between the
physical energy dissipation sustaining a nonequilibrium system and a measure of
statistical irreversibility (arrow of time), can provide quantitative insight
into the mechanisms of nonequilibrium activity across scales. Specifically, we
introduce a multiscale irreversibility metric and demonstrate how it can be
used to extract model-independent estimates of dissipative timescales. Using
this metric, we measure the dissipation timescale of a multiscale cellular
structure - the actomyosin cortex - and further observe that the
irreversibility metric maintains a monotonic relationship with the underlying
biological nonequilibrium activity. Additionally, the irreversibility metric
can detect shifts in the dissipative timescales when we induce spatiotemporal
patterns of biochemical signaling proteins upstream of actomyosin activation.
Our experimental measurements are complemented by a theoretical analysis of a
generic class of nonequilibrium dynamics, elucidating how dissipative
timescales manifest in multiscale irreversibility.
