Onsager regression characterizes living systems in passive measurements
Understanding life is arguably among the most complex scientific problems faced in modern research. From a physics perspective, living systems are complex dynamic entities that operate far from thermodynamic equilibrium.1-3 This active, non-equilibrium behaviour, with its constant hunger for energy, allows life to overcome the ever dispersing forces of entropy, and drives cellular organisation.4, 5 Unfortunately, most analysis methods provided by the toolbox of statistical mechanics cannot be used in such non-equilibrium situations, forcing researchers to use sophisticated and often invasive approaches to study the mechanistic processes inside living organisms. Here we introduce a new observable coined the mean back relaxation. Based on three-point probabilities, and exploiting Onsagers regression hypothesis, it extracts additional information from passively observed trajectories compared to classical observables such as the mean squared displacement. We mathematically prove that the mean back relaxation is able to detect broken detailed balance in systems confined in stationary or actively diffusing potentials. We show in experiment and theory that it gives access to the non-equilibrium generating energy and the viscoelastic material properties of a well controlled artificial system, and we experimentally demonstrate that it does so even for a variety of living systems, revealing an astonishing relation between the mean back relaxation and the active mechanical energy. Based on these findings, we conclude that it acts as a new marker of non-equilibrium dynamics. Combining, in a next step, passive fluctuations with the extracted active energy allows to overcome a fundamental barrier in the study of living systems; it gives access to the viscoelastic material properties from passive measurements.