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Register a new userActive matter: quantifying the departure from equilibrium
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Active matter systems are driven out of equilibrium at the level of individual constituents. One widely studied class are systems of athermal particles that move under the combined influence of interparticle interactions and self-propulsions, with the latter evolving according to the Ornstein-Uhlenbeck stochastic process. Intuitively, these so-called active Ornstein-Uhlenbeck particles (AOUPs) systems are farther from equilibrium for longer self-propulsion persistence times. Quantitatively, this is confirmed by the increasing equal-time velocity correlations (which are trivial in equilibrium) and by the increasing violation of the Einstein relation between the self-diffusion and mobility coefficients. In contrast, the entropy production rate, calculated from the ratio of the probabilities of the position space trajectory and its time-reversed counterpart, has a non-monotonic dependence on the persistence time. Thus, it does not properly quantify the departure of AOUPs systems from equilibrium.
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Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of active matter in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines.
Despite their fundamentally non-equilibrium nature, the individual and collective behavior of active systems with polar propulsion and isotropic interactions (polar-isotropic active systems) are remarkably well captured by equilibrium mapping techniques. Here we examine two signatures of equilibrium systems -- the existence of a local free energy function and the independence of the coarse- grained behavior on the details of the microscopic dynamics -- in polar-isotropic active particles confined by hard walls of arbitrary geometry at the one-particle level. We find that boundaries that possess concave regions make the density profile strongly dynamics-dependent and give it a nonlocal dependence on the geometry of the confining box. This in turn constrains the scope of equilibrium mapping techniques in polar-isotropic active systems.
We follow the dynamics of an ensemble of interacting self-propelled motorized particles in contact with an equilibrated thermal bath. We find that the fluctuation-dissipation relation allows for the definition of an effective temperature that is compatible with the results obtained using a tracer particle as a thermometer. The effective temperature takes a value which is higher than the temperature of the bath and it is continuously controlled by the motor intensity.
Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature active matter systems exist in nonequilibrium states. In this paper the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collectively to form structures such as dynamic clusters. A general nonequilibrium thermodynamics framework for the description of such systems is presented that accounts for both self-diffusiophoresis and diffusiophoresis due to external concentration gradients, and is consistent with microreversibility. It predicts the existence of a reciprocal effect of diffusiophoresis back onto the reaction rate for the entire collection of colloids in the system, as well as the existence of a clustering instability that leads to nonequilibrium inhomogeneous system states.
This article summarizes some of the open questions in the field of active matter that have emerged during Active20, a nine-week program held at the Kavli Institute for Theoretical Physics (KITP) in Spring 2020. The article does not provide a review of the field, but rather a personal view of the authors, informed by contributions of all participants, on new directions in active matter research. The topics highlighted include: the ubiquitous occurrence of spontaneous flows and active turbulence and the theoretical and experimental challenges associated with controlling and harnessing such flows; the role of motile topological defects in ordered states of active matter and their possible biological relevance; the emergence of non-reciprocal effective interactions and the role of chirality in active systems and their intriguing connections to non-Hermitian quantum mechanics; the progress towards a formulation of the thermodynamics of active systems thanks to the feedback between theory and experiments; the impact of the active matter framework on our understanding of the emergent mechanics of biological tissue. These seemingly diverse phenomena all stem from the defining property of active matter - assemblies of self-driven entities that individually break time-reversal symmetry and collectively organize in a rich variety of nonequilibrium states.
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