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  • Review Article
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Time irreversibility in active matter, from micro to macro

Nature Reviews Physics volume 4, pages 167–183 (2022)Cite this article

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Abstract

Active matter encompasses systems whose individual constituents dissipate energy to exert propelling forces on their environment. These systems exhibit dynamical phenomena with no counterpart in passive systems. In this Review, we disentangle the respective roles of the arrow of time and the non-Boltzmann nature of steady-state fluctuations in this rich phenomenology. We show that effective, time-reversible descriptions of active systems may be found at all scales and discuss how interactions, either between constituents or with external operators, may reveal the nonequilibrium nature of the microscopic source of energy. At a time when engineering active materials appears to be becoming possible, we argue that methods stemming from equilibrium statistical mechanics may guide the design of new active materials.

Key points

  • Active systems comprise entities that dissipate energy to exert forces on their environment. This energy flux drives them far from thermal equilibrium. As such, their steady state escapes Boltzmann statistics and their dynamics breaks time-reversal symmetry.

  • The entropy production rate is a versatile tool to quantify the departure of active systems from equilibrium.

  • At the single-particle level, the entropy production rate reveals violations of time-reversal symmetry that depend on the level of coarse graining.

  • The breakdown of time-reversal symmetry and the departure from the Boltzmann distribution are responsible for a rich phenomenology in active systems, with no counterparts in equilibrium.

  • In the presence of obstacles or external potentials, the departure from the Boltzmann distribution is reflected by a non-local steady-state distribution, accompanied by probability currents, even in the dilute limit.

  • Systems of interacting active particles exhibit rich collective behaviours. Depending on the level of coarse graining, some active systems may be mapped onto equilibrium ones, leading to generalized thermodynamics with non-trivial state functions.

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Fig. 1: Active matter systems are commonly found in nature and engineered in the laboratory.
Fig. 2: Difference between forces on passive and active particles in a fluid.
Fig. 3: Trajectories of a run-and-tumble particle experiencing thermal noise.
Fig. 4: Ratchet effects in active matter.
Fig. 5: Motility-induced phase separation.

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Acknowledgements

J.O., J.T. and F.v.W. acknowledge support from ANR grant THEMA; Y.K. acknowledges support from an Israel Science Foundation grant (1331/17) and an NSF-BSF grant (2016624). The authors thank M. Pica Ciamarra and Y. Li for sharing the data that were used to calibrate the simulations shown in Fig. 5a. The authors benefited from participation in the 2020 KITP program on Active Matter supported by the grant NSF PHY-1748958.

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  1. Université de Paris, MSC, UMR 7057 CNRS, Paris, France

    J. O’Byrne, J. Tailleur & F. van Wijland

  2. Department of Physics, Technion, Haifa, Israel

    Y. Kafri

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O’Byrne, J., Kafri, Y., Tailleur, J. et al. Time irreversibility in active matter, from micro to macro. Nat Rev Phys 4, 167–183 (2022). https://doi.org/10.1038/s42254-021-00406-2

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