Hidden entropy production and work fluctuations in an ideal active gas

Microscopic origins of the swim pressure and the anomalous surface tension of active matter

The unique pressure exerted by active particles-the "swim" pressure-has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density-an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an "equivalent pressure" (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied.

Stochastic thermodynamics for self-propelled particles

We propose a generalization of stochastic thermodynamics to systems of active particles, which move under the combined influence of stochastic internal self-propulsions (activity) and a heat bath. The main idea is to consider joint trajectories of particles' positions and self-propulsions. It is then possible to exploit formal similarity of an active system and a system consisting of two subsystems interacting with different heat reservoirs and coupled by a nonsymmetric interaction. The resulting thermodynamic description closely follows the standard stochastic thermodynamics. In particular, total entropy production, Δs_{tot}, can be decomposed into housekeeping, Δs_{hk}, and excess, Δs_{ex}, parts. Both Δs_{tot} and Δs_{hk} satisfy fluctuation theorems. The average rate of the steady-state housekeeping entropy production can be related to the violation of the fluctuation-dissipation theorem via a Harada-Sasa relation. The excess entropy production enters into a Hatano-Sasa-like relation, which leads to a generalized Clausius inequality involving the change of the system's entropy and the excess entropy production. Interestingly, although the evolution of particles' self-propulsions is free and uncoupled from that of their positions, nontrivial steady-state correlations between these variables lead to the nonzero excess dissipation in the reservoir coupled to the self-propulsions.

Irreversibility and emergent structure in active matter

Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft matter exhibiting complex collective phenomena, yet the thermodynamics of such systems remain poorly understood. In this article we study the dynamical irreversibility of large-scale active systems capable of motility-induced phase separation and polar alignment. We use a model with momenta in both translational and rotational degrees of freedom, revealing a hidden component not previously reported in the literature. Steady-state irreversibility is quantified at each point in the phase diagram which exhibits sharp discontinuities at phase transitions. Identification of the irreversibility in individual particles lays the groundwork for discussion of the thermodynamics of microfeatures, such as defects in the emergent structure. The interpretation of the time reversal symmetry in the dynamics of the particles is found to be crucial.

Response of active Brownian particles to boundary driving

We computationally study the behavior of underdamped active Brownian particles in a sheared channel geometry. Due to their underdamped dynamics, the particles carry momentum a characteristic distance away from the boundary before it is dissipated into the substrate. We correlate this distance with the persistence of particle trajectories, determined jointly by their friction and self-propulsion. Within this characteristic length, we observe counterintuitive phenomena stemming from the interplay of activity, interparticle interactions, and the boundary driving. Depending on the values of friction and self-propulsion, interparticle interactions can either aid or hinder momentum transport. More dramatically, in certain cases we observe a flow reversal near the wall, which we correlate with an induced polarization of the particle self-propulsion directions. We rationalize these results in terms of a simple kinetic picture of particle trajectories.

Guided active particles

To account for the possibility of an externally driven taxis in active systems, we develop a model of a guided active drift which relies on the presence of an external guiding field and a vectorial coupling between the mechanical degrees of freedom and a chemical reaction. To characterize the ability of guided active particles to carry cargo, we generalize the notion of Stokes efficiency extending it to the case of stall conditions. To show the generality of the proposed mechanism, we discuss guided electric circuits capable of turning fluctuations into a directed current without a source of voltage.

On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems

We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.

Additivity and density fluctuations in Vicsek-like models of self-propelled particles

We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a fluctuation-response relation-the direct consequence of an additivity property-we compute logarithm of the large-deviation probabilities of the coarse-grained subsystem density, while the system is in the disordered fluid phase with vanishing macroscopic velocity. The large-deviation probabilities, computed within additivity, agree remarkably well with that obtained from direct microscopic simulations of the models. Our results provide evidence of the existence of an equilibriumlike chemical potential, which governs the coarse-grained density fluctuations in the Vicsek-like models. Moreover, comparison of the particle-number fluctuations among several self-propelled particle systems suggests a common mechanism through which the number fluctuations arise in such systems.

Active particles in noninertial frames: How to self-propel on a carousel

Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.

Optimizing active work: Dynamical phase transitions, collective motion, and jamming

Active work measures how far the local self-forcing of active particles translates into real motion. Using population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.