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Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.
In addition to thermal effects, active processes can strongly impact the stochastic dynamics of a system8,9,10,11,12. Recently, there has been a growing interest in quantifying and characterizing the non-equilibrium nature of the stochastic dynamics in active soft and living systems13,14,15,16,17,18,19,20,21,22,23,24,25. In cells, molecular-scale activity, powered for instance by ATP hydrolysis, controls mesoscale non-equilibrium processes in assemblies, such as cilia26,27, flagella28, chromosomes29, protein droplets30, or cytoskeletal networks31,32,33,34. The irreversible nature of such non-equilibrium processes can lead to measurable dissipative currents in a phase space of mesoscopic degrees of freedom9,17,18,35,36,37,38. Such dissipative currents can be quantified by the entropy production rate39, which is a measure of the irreversibility of the dynamics40. New approaches have been developed to measure this rate in real systems22,24, shedding light onto the structure of dissipative processes19 and their impact on the dynamics of living matter20. However, it remains an outstanding challenge to accurately infer the entropy production rate by analyzing Brownian movies of such systems.
Thus, with sufficient information, we can use our approach to accurately predict at any instant of time the physical force fields in image space from the Brownian movie, even if the system is out of equilibrium. Moreover, the results for this simple two-bead system demonstrate the validity of our approach: we reliably infer the non-equilibrium dynamics of this system. Arguably, direct tracking of the two beads is, in this case, a more straightforward approach. However, this changes when considering more general soft assemblies comprised of many degrees of freedom.
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