In complex systems, external parameters often determine the phase in which the system operates, that is, its macroscopic behaviour. For nearly a century, statistical physics has been used to extensively study systems’ transitions across phases, (universal) critical exponents and related dynamical properties. Here we consider the functionality of systems, particularly operations in socio-technical ones, production in economic ones and, more generally, any schedule-based system, where timing is of crucial importance. We introduce a stylized model of delay propagation on temporal networks, where the magnitude of the delay-mitigating buffer acts as a control parameter. The model exhibits timeliness criticality, a novel form of critical behaviour. We characterize fluctuations near criticality, commonly referred to as avalanches, and identify the corresponding critical exponents. The model exhibits timeliness criticality also when run on real-world temporal systems such as production networks. Additionally, we explore potential connections with the mode-coupling theory of glasses, depinning transition and directed polymer problem.


Moran, J., Romeijnders, M., Le Doussal, P., Pijpers, F.P., Weitzel, U., Panja, D., & Bouchaud, J-P, (2024), 'Timeliness criticality in complex systems', nature physics, https://doi.org/10.1038/s41567-024-02525-w.
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