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Abstract We propose and investigate a method for identifying timescales of dissipation in nonequilibrium steady states modeled as discrete-state Markov jump processes. The method is based on how the irreversibility—measured by the statistical breaking of time-reversal symmetry—varies under temporal coarse-graining. We observe a sigmoidal-like shape of the irreversibility as a function of the coarse-graining time whose functional form we derive for systems with a fast driven transition. This theoretical prediction allows us to develop a method for estimating the dissipative time scale from time-series data by fitting estimates of the irreversibility to our predicted functional form. We further analyze the accuracy and statistical fluctuations of this estimate. 

The name active matter refers to any collection of entities that individually use free energy to generate their own motion and forces. Through interactions, active particles spontaneously organize in emergent large-scale structures with a rich range of materials properties. The active matter paradigm has been applied to living and non-living systems over a vast dynamic range, from the organization of subnuclear structures in the cell to collective motion at the human scale. The diverse phenomena exhibited by these systems all stem from the defining property of active matter as an assembly of components that individually and dissipatively break time-reversal symmetry. This article outlines a selection of current and emerging directions in active matter research. It aims at providing a pedagogical and forward looking introduction for researchers new to the field and a roadmap of open challenges and future directions that may appeal to those established in the area. 

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and it has been extensively studied in the context of topological quantum computation. In living systems, topological defects are crucial for the localization and organization of biochemical signaling waves, but their braiding dynamics remain unexplored. Here, we show that the spiral wave cores, which organize the Rho-GTP protein signaling dynamics and force generation on the membrane of starfish egg cells, undergo spontaneous braiding dynamics. Experimentally measured world line braiding exponents and topological entropy correlate with cellular activity and agree with predictions from a generic field theory. Our analysis further reveals the creation and annihilation of virtual quasi-particle excitations during defect scattering events, suggesting phenomenological parallels between quantum and living matter.