Using relative entropy to quantify non-equilibrium activity in biological active matter

Stochastic force generation within cells drive the system out-of-equilibrium. These forces play a crucial role in vital processes such as intracellular transport. It is important to characterize the nature of such nonequilibrium steady states to understand cellular dynamics and function. Here we apply a framework based on the notion of relative entropy or Kullbeck-Leibler Divergence (KLD) to quantify the extent of non-equilibrium activity in biological active matter. In this framework, from the data of a single stationary trajectory obtained sampling any physical variable of the system, we can estimate the average dissipation rate of the mechanism that generated the data. We validate our framework numerically by using hidden Markov models to simulate different levels of out-of-equilibrium cellular activity. Using experimental time series data of probe particles embedded in the actomyosin cortices, we establish a lower bound for the entropy production of cortical activity. Our results demonstrate a reliable way to quantify the non-equilibrium activity in mesoscopic systems.