Phase transition in protocols minimizing work fluctuations

For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade-off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal work protocols, which therefore never become quasistatic.Comment: 6 pages, 6 figures + SI as ancillary fil

From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations

We show that the flocking transition in the Vicsek model is best understood as a liquid-gas transition, rather than an order-disorder one. The full phase separation observed in flocking models with Z2 rotational symmetry is, however, replaced by a microphase separation leading to a smectic arrangement of traveling ordered bands. Remarkably, continuous deterministic descriptions do not account for this difference, which is only recovered at the fluctuating hydrodynamics level. Scalar and vectorial order parameters indeed produce different types of number fluctuations, which we show to be essential in selecting the inhomogeneous patterns. This highlights an unexpected role of fluctuations in the selection of flock shapes.Comment: 5 p., 5 fig.. Supplementary material: 7 movie

Non-equilibrium forces following quenches in active and thermal matter

Non-equilibrium systems are known to exhibit long-ranged correlations due to conservation of quantities like density or momentum. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of non-equilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent {\it density-induced forces}. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient {\it fluctuation-induced forces} emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Finally, we propose several scenarios for their experimental observation.Comment: - Added Journal reference and DOI - Modified title - Fixed minor typos - Added plot of Eq. (32) [16 pages, 11 figures

Response of active Brownian particles to shear flow

We study the linear response of interacting active Brownian particles in an external potential to simple shear flow. Using a path integral approach, we derive the linear response of any state observable to initiating shear in terms of correlation functions evaluated in the unperturbed system. For systems and observables which are symmetric under exchange of the $x$ and $y$ coordinates, the response formula can be drastically simplified to a form containing only state variables in the corresponding correlation functions (compared to the generic formula containing also time derivatives). In general, the shear couples to the particles by translational as well as rotational advection, but in the aforementioned case of $xy$ symmetry only translational advection is relevant in the linear regime. We apply the response formulas analytically in solvable cases and numerically in a specific setup. In particular, we investigate the effect of a shear flow on the morphology and the stress of $N$ confined active particles in interaction, where we find that the activity as well as additional alignment interactions generally increase the response.Comment: 13 pages, 4 figure

Mechanical pressure and momentum conservation in dry active matter

We relate the breakdown of equations of states for the mechanical pressure of generic dry active systems to the lack of momentum conservation in such systems. We show how sources and sinks of momentum arise generically close to confining walls. These typically depend on the interactions of the container with the particles, which makes the mechanical pressure a container-dependent quantity. We show that an equation of state is recovered if the dynamics of the orientation of active particles are decoupled from other degrees of freedom and lead to an apolar bulk steady-state. This is related to the fact that the mean steady-state active force density is the divergence of the flux of "active impulse", an observable which measures the mean momentum particles will receive from the substrate in the future

Generic long-range interactions between passive bodies in an active fluid

Because active particles break time-reversal symmetry, a single non-spherical body placed in an active fluid generates currents. We show that when two or more passive bodies are placed in an active fluid these currents lead to long-range interactions. Using a multipole expansion we characterize their leading-order behaviors in terms of single-body properties and show that they decay as a power law with the distance between the bodies, are anisotropic, and do not obey an action--reaction principle. The interactions lead to rich dynamics of the bodies, illustrated by the spontaneous synchronized rotation of pinned non-chiral bodies and the formation of traveling bound pairs. The occurrence of these phenomena depends on tunable properties of the bodies, thus opening new possibilities for self-assembly mediated by active fluids.Comment: 21 pages, 6 figure

Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles

Motility-induced phase separation (MIPS) leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss its application to active particles interacting either via quorum-sensing interactions or directly through pairwise forces.Comment: 33 pages, 14 figure

Physique statistique de la matière active

Active systems, composed of particles capable of using the energy stored in theirmedium to self-propel, are ubiquitous in nature. They are found at all scales :from molecular motors to cellular tissues, bacterial colonies and animal groups.These out-of-equilibrium systems have attracted a lot of attention from the physicscommunity because they show a richer phenomenology than passive systems thatwe can still understand using simple models.In this thesis, we study analytically and numerically minimal models of activeparticles. They allow us to understand different phenomena that are characteristicof active matter and to study the large-scale behavior of several classes of systems.The thermodynamics of active systems is fundamentally different from thatof equilibrium systems. In particular, we show that the mechanical pressure ofan active particle fluid is not given by an equation of state. The pressure isnot a property of the fluid and depends on the details of the interaction with thecontaining vessel.We also study two phase transitions that specific to active matter : The motility-induced phase separation and the transition to collective motion. In both cases, weobserve a phase separation between a liquid and a gas and study their coexistence.For the transition to collective motion, we exhibit two universality classes, basedon the particles’ symmetry, which have different types of coexistence phases.Les systèmes actifs, composés de particules capables de transformer l’énergiestockée dans leur environnement pour s’autopropulser, sont omniprésents dans lanature. On les trouve à toutes les échelles : des moteurs moléculaires aux groupesd’animaux, en passant par les tissus cellulaires et les colonies de bactéries. Cessystèmes hors d’équilibre ont attiré l’attention des physiciens car ils présententune phénoménologie plus riche que les systèmes passifs, que l’on peut cependantcomprendre à partir de modèles simples.Dans cette thèse, nous avons étudié analytiquement et numériquement desmodèles minimaux de particules actives. Ceux-ci nous ont permis de comprendredifférents phénomènes spécifiques à la matière active et d’étudier le comportementà grand échelle de plusieurs classes de systèmes.La thermodynamique des systèmes actifs est fondamentalement différente decelle des systèmes d’équilibre. Nous montrons en particulier que la pression méca-nique d’un fluide de particules actives n’est pas donnée par une équation d’état.La pression n’est donc pas seulement une propriété du fluide et dépend du détaildes interactions avec les parois du récipient dans lequel il est confiné.Nous étudions également deux transitions de phase propres à la matière active :la séparation de phase induite par la motilité et la transition vers le mouvementcollectif. Dans les deux cas, on observe une séparation de phase entre un liquideet un gaz dont nous étudions la coexistence. Pour la transition vers le mouvementcollectif on distingue deux classes d’universalité, en fonction de la symétrie desparticules, qui ont des coexistences de phase différentes

Sedimentation of self-propelled Janus colloids: polarization and pressure

We study experimentally-using Janus colloids-and theoretically-using Active Brownian Particles- the sedimentation of dilute active colloids. We first confirm the existence of an exponential density profile. We show experimentally the emergence of a polarized steady state outside the effective equilibrium regime, i.e. when v_s is not much smaller than the propulsion speed. The experimental distribution of polarization is very well described by the theoretical prediction with no fitting parameter. We then discuss and compare three different definitions of pressure for sedimenting particles: the weight of particles above a given height, the flux of momentum and active impulse, and the force density measured by pressure gauges

Towards Distance-Based Phylogenetic Inference in Average-Case Linear-Time

Computing genetic evolution distances among a set of taxa dominates the running time of many phylogenetic inference methods. Most of genetic evolution distance definitions rely, even if indirectly, on computing the pairwise Hamming distance among sequences or profiles. We propose here an average-case linear-time algorithm to compute pairwise Hamming distances among a set of taxa under a given Hamming distance threshold. This article includes both a theoretical analysis and extensive experimental results concerning the proposed algorithm. We further show how this algorithm can be successfully integrated into a well known phylogenetic inference method