Dominance of extreme statistics in a prototype many-body Brownian ratchet

Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in filaments' spatial distribution.Comment: 5 pages with 3 figures + 20 pages of Supplementary Material with 2 figures. Updated to agree with published version; published as a Communication in J. Chem. Phy

On the microscopic origin and macroscopic implications of lane formation in mixtures of oppositely-driven particles

Colloidal particles of two types, driven in opposite directions, can segregate into lanes [Vissers et al. Soft Matter 7, 2352 (2011)]. This phenomenon can be reproduced by two-dimensional Brownian dynamics simulations of model particles [Dzubiella et al. Phys. Rev. E 65, 021402 (2002)]. Here we use computer simulation to assess the generality of lane formation with respect to variation of particle type and dynamical protocol. We find that laning results from rectification of diffusion on the scale of a particle diameter: oppositely-driven particles must, in the time taken to encounter each other in the direction of the drive, diffuse in the perpendicular direction by about one particle diameter. This geometric constraint implies that the diffusion constant of a particle, in the presence of those of the opposite type, grows approximately linearly with Peclet number, a prediction confirmed by our numerics over a range of model parameters. Such environment-dependent diffusion is statistically similar to an effective interparticle attraction; consistent with this observation, we find that oppositely-driven non-attractive colloids display features characteristic of the simplest model system possessing both interparticle attractions and persistent motion, the driven Ising lattice gas [Katz, Leibowitz, Spohn, J. Stat. Phys. 34, 497 (1984)]. These features include long-ranged correlations in the disordered regime, and a critical regime characterized by a change in slope of the particle current with Peclet number and by fluctuations that grow with system size. By analogy, we suggest that lane formation in the driven colloid system is in the macroscopic limit a phase transition, but that macroscopic phase separation would not occur in finite time upon starting from disordered initial conditions

Near-optimal protocols in complex nonequilibrium transformations

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols which minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased towards a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.Comment: 6 pages and 3 figures plus 4 pages and 5 figures of supplemental materia

Efficiency and Large Deviations in Time-Asymmetric Stochastic Heat Engines

In a stochastic heat engine driven by a cyclic non-equilibrium protocol, fluctuations in work and heat give rise to a fluctuating efficiency. Using computer simulations and tools from large deviation theory, we have examined these fluctuations in detail for a model two-state engine. We find in general that the form of efficiency probability distributions is similar to those described by Verley et al. [2014 Nat Comm, 5 4721], in particular featuring a local minimum in the long-time limit. In contrast to the time-symmetric engine protocols studied previously, however, this minimum need not occur at the value characteristic of a reversible Carnot engine. Furthermore, while the local minimum may reside at the global minimum of a large deviation rate function, it does not generally correspond to the least likely efficiency measured over finite time. We introduce a general approximation for the finite-time efficiency distribution, $P(\eta)$, based on large deviation statistics of work and heat, that remains very accurate even when $P(\eta)$ deviates significantly from its large deviation form.Comment: 10 pages, 3 figure