Onsager regression characterizes living systems in passive measurements

Abstract

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 thermo-dynamic 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 hence drives cellular organisation and dynamics at the micrometer scale.4,5 Unfortunately, most analysis methods provided by the powerful 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, that allows simple detection of broken detailed balance and full quantification of the active mechanics from passively observed particle trajectories. Based on three-point probabilities and exploiting Onsager’s regression hypothesis, the mean back relaxation extracts more information from passively measurements compared to classical observables such as the mean squared displacement. We show that it gives access to the non-equilibrium generating energy and the viscoelastic material properties of a well controlled artificial system, and, surprisingly, also of a variety of living systems. It thus acts as a new marker of non-equilibrium dynamics, a statement based on an astonishing relation between the mean back relaxation and the active mechanical energy. 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.