Hydrodynamic memory can boost enormously driven nonlinear diffusion and transport

Effects of Hydrodynamic Backflow on the Transmission Coefficient of a Barrier-Crossing Brownian Particle

The slow power law decay of the velocity autocorrelation function of a particle moving stochastically in a condensed-phase fluid is widely attributed to the momentum that fluid molecules displaced by the particle transfer back to it during the course of its motion. The forces created by this backflow effect are known as Basset forces, and they have been found in recent analytical work and numerical simulations to be implicated in a number of interesting dynamical phenomena, including boosted particle mobility in tilted washboard potentials. Motivated by these findings, the present paper is an investigation of the role of backflow in thermally activated barrier crossing, the governing process in essentially all condensed-phase chemical reactions. More specifically, it is an exact analytical calculation, carried out within the framework of the reactive-flux formalism, of the transmission coefficient κ(t) of a Brownian particle that crosses an inverted parabola under the influence of a colored noise process originating in the Basset force and a Markovian time-local friction. The calculation establishes that κ(t) is significantly enhanced over its backflow-free limit.

Activity-Induced Enhancement of Superdiffusive Transport in Bacterial Turbulence

Superdiffusion processes significantly promote the transport of tiny passive particles within biological fluids. Activity, one of the essential measures for living matter, however, is less examined in terms of how and to what extent it can improve the diffusivity of the moving particles. Here, bacterial suspensions are confined within the microfluidic channel at the state of bacterial turbulence, and are tuned to different activity levels by oxygen consumption in control. Systematic measurements are conducted to determine the superdiffusion exponent, which characterizes the diffusivity strength of tracer particles, depending on the continuously injecting energy converted to motile activity from swimming individuals. Higher activity is quantified to drastically enhance the superdiffusion process of passive tracers in the short-time regime. Moreover, the number density of the swimming bacteria is controlled to contribute to the field activity, and then to strengthen the super-diffusivity of tracers, distinguished by regimes with and without collective motion of interacting bacteria. Finally, the non-slip surfaces of the microfluidic channel lower the superdiffusion of immersed tracers due to the resistance, with the small diffusivity differing from the counterpart in the bulk. The findings here suggest ways of controlled diffusion and transport of substances within the living system with different levels of nutrition and resources and boundary walls, leading to efficient mixing, drug delivery and intracellular communications.

Conundrum of weak-noise limit for diffusion in a tilted periodic potential

The weak-noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity, frequently hidden in deterministic systems, to give rise to phenomena that are absent for both noiseless and strong fluctuations regimes. Unfortunately, this limit is also notoriously hard to approach analytically or numerically. We reinvestigate in this context the paradigmatic model of nonequilibrium statistical physics consisting of inertial Brownian particles diffusing in a tilted periodic potential by exploiting state-of-the-art computer simulations of an extremely long timescale. In contrast to previous results on this longstanding problem, we draw an inference that in the parameter regime for which the particle velocity is bistable the lifetime of ballistic diffusion diverges to infinity when the thermal noise intensity tends to zero, i.e., an everlasting ballistic diffusion emerges. As a consequence, the diffusion coefficient does not reach its stationary constant value.

Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion

In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.

Arcsine law and multistable Brownian dynamics in a tilted periodic potential

Multistability is one of the most important phenomena in dynamical systems, e.g., bistability enables the implementation of logic gates and therefore computation. Recently multistability has attracted a greatly renewed interest related to memristors and graphene structures, to name only a few. We investigate tristability in velocity dynamics of a Brownian particle subjected to a tilted periodic potential. It is demonstrated that the origin of this effect is attributed to the arcsine law for the velocity dynamics at the zero temperature limit. We analyze the impact of thermal fluctuations and construct the phase diagram for the stability of the velocity dynamics. It suggests an efficient strategy to control the multistability by changing solely the force acting on the particle or temperature of the system. Our findings for the paradigmatic model of nonequilibrium statistical physics apply to, inter alia, Brownian motors, Josephson junctions, cold atoms dwelling in optical lattices, and colloidal systems.

Introducing Memory in Coarse-Grained Molecular Simulations

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.