We study a system of purely repulsive spherical self-propelled particles in the minimal set-up inducing Motility-Induced Phase Separation (MIPS). We show that, even if explicit alignment interactions are absent, a growing order in the velocities of the clustered particles accompanies MIPS. Particles arrange into aligned or vortex-like domains. Their sizes increase as the persistence of the self-propulsion grows, an effect that is quantified studying the spatial correlation function of the velocities. We explain the velocity-alignment by unveiling a hidden alignment interaction of the Vicsek-like form, induced by the interplay between steric interactions and self-propulsion. As a consequence, we argue that the MIPS transition cannot be fully understood in terms of a scalar field, the density, since the collective orientation of the velocities should be included in effective coarse-grained descriptions. Fishes [1], birds [2] or insects [3] often display fashinating collective behaviors such as flocking [2, 4] and swarming [5], where all units of a group move coherently producing intriguing dynamical patterns. A different mode of organization of living organisms is clustering, for instance in bacterial colonies [6], such as E. Coli [7], Myxococcus xanthus [8] or Thiovulum majus [9], relevant for histological cultures in several areas of medical and pharmaceutical sciences. Out of the biological realm, the occurrence of stable clusters [10-13], stable chains [14] or vortices [15] in activated colloidal particles, e.g. autophoretic colloids or Janus disks [16,17], offers an interesting challenge for the design of new materials.Even if the microscopic details differ case by case, a few classes of minimal models with common coarsegrained features have been introduced in statistical physics. Units in these models are called "active" or "selfpropelled" particles [18-20] to differentiate them from Brownian colloids which passively obey the forces of the surrounding environment. Propelling forces may be either of mechanical origin (flagella or body deformation), or of thermodynamic nature (diffusiophoresis and selfelectrophoresis) [21,22]. In some simple and effective examples, self-propulsion is modeled as a constant force with stochastic orientation, as in the case of Active Brownian Particles (ABP) [23,24]. Thermal fluctuations play only a marginal role and stochasticity is usually due to the unsteady nature of the swimming force itself.It is well-known that dumbells, rods and, in general, elongated microswimmers display a marked orientational order even in the absence of alignment interactions [25][26][27][28]. Instead, in the literature, it is believed that explicit aligning velocity-interactions are crucial to observe velocity alignment between spherical self-propelled units [29]. This kind of interaction, such as that in the seminal Vicsek model [30], consists in a short-range force that aligns the velocity of a target particle to the average of the neighboring ones. Vicsek interactions lead to long-range polar order...
By employing a path integral formulation, we obtain the entropy production rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the presence and in the absence of thermal noise. The present treatment clarifies some contraddictions concerning the definition of the entropy production rate in the AOUP model, recently appeared in the literature. We derive explicit formulas for three dierent cases: overdamped Brownian particle, AOUP with and without thermal noise. In addition, we show that it is not necessary to introduce additional hypotheses concerning the parity of auxiliary variables under time reversal transformation. Our results agree with those based on a previous mesoscopic approach.
We consider the effect of geometric confinement on the steady-state properties of a one-dimensional active suspension subject to thermal noise. The random active force is modeled by an Ornstein-Uhlenbeck process and the system is studied both numerically, by integrating the Langevin governing equations, and analytically by solving the associated Fokker-Planck equation under suitable approximations. The comparison between the two approaches displays a fairly good agreement and in particular, we show that the Fokker-Planck approach can predict the structure of the system both in the wall region and in the bulk-like region where the surface forces are negligible. The simultaneous presence of thermal noise and active forces determines the formation of a layer, extending from the walls towards the bulk, where the system exhibits polar order. We relate the presence of such ordering to the mechanical pressure exerted on the container's walls and show how it depends on the separation of the boundaries and determines a Casimir-like attractive force mediated by the active suspension.
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