Nonequilibrium noise emerging from broken detailed balance in active gels

In thermodynamic equilibrium, the fluctuation-dissipation theorem links thermal fluctuations and dissipation. Biological systems, however, are driven out of equilibrium by internal processes that produce additional, active fluctuations. Despite being relevant for biological functions such as intracellular transport, predicting the statistical properties of active fluctuations remains challenging. Here, we address this challenge in a minimal model of an active gel as a network of elastic elements connected by transient crosslinks. The crosslinkers' binding and unbinding rates break detailed balance, which drives the system out of equilibrium. Through coarse-graining, we derive fluctuating hydrodynamic equations including an active noise term, which emerges explicitly from the breaking of detailed balance. Finally, we provide predictions for the stochastic motion of a tracer particle embedded in the active gel, which enables comparisons with microrheology experiments both in synthetic active gels and in cells. Overall, our work provides an explicit link between the statistical properties of active fluctuations and the molecular breaking of detailed balance. Thus, it paves the way toward complementing the fluctuation-dissipation theorem with a fluctuation-activity relation in active systems.