Session S09: Noise-Driven Dynamics in Far-From-Equilibrium Systems I

Noise-driven phenomena on the dynamics of levitated nanoparticles

Micro and nanoparticles can be individually manipulated by different trapping mechanisms, among which optical tweezers and Paul traps are the most extended approaches. Trapped particles are subject to Brownian motion, due to collisions with water or gas molecules, depending on the dispersing medium. Once trapped, the particles can be driven out of equilibrium under the action of external fields, giving rise to very rich dynamics. In this talk, we will discuss some of our work with trapped nanoparticles dispersed in different media, including water, air, and vacuum. We will show that exquisite control over the dynamics can be achieved by using state-of-the-art instrumentation, thanks to the sensitivity over position and forces that these provide. Our most recent results are related to the observation of the Kovacs effect on the energy of a levitated nanoparticle, a memory effect first observed in polymers. According to this effect, the thermalization of a nanoparticle can follow a non-monotonic path due to the inertia of the system.    

Active matter under control

Active matter consumes fuel in order to sustain individual motion. This gives rise to interesting collective effects, such as motility induced phase separation, a hallmark of active matter. Currently, we lack a physical framework that predicts the best protocol for driving active systems between different states in a way that optimizes the dissipated energy. Indeed, existing equilibrium thermodynamics is an inadequate foundation to build a framework of control for active systems due to the constant consumption of fuel. Here, we derive and implement a nonequilibrium thermodynamic framework, using response theory, to optimally control active systems.   

Anomalous cooling without metastability

Since the temperature of an object that cools decreases as it relaxes to thermal equilibrium, one would naively expect a hot object to take longer to cool than a warm one. However, as long observed, sometimes hot water can cool and begin to freeze faster than cold water.  Previous confirmed observations of this anomalous thermal relaxation (the "Mpemba effect") have all involved either a true phase transition (such as water freezing to ice) or at least a metastable state.  The typical mechanism is that the system is quickly trapped in a long-lived intermediate state.  Specially chosen initial conditions whose dynamical trajectories in state space can avoid this intermediate state can then relax exponentially faster than the typical state, which is caught in the long-lived intermediate state.  In previous work, we have shown that it is possible to reliably and reproducibly observe the Mpemba effect in a system consisting of a single micron-sized, colloidal particle diffusing in water and moving in a tilted double-well potential.  The higher well of the potential corresponds to a coarse-grained metastable state.  Here we show that anomalous relaxation can be observed in a potential that has only a single local minimum.  We discuss possible mechanisms explaining this effect.   

Effective thermal equilibrium induced by crosslinking proteins in polymer chromosome model

Biological systems under the influence of microscale active agents such as proteins are frequently modeled using switching forces as the agents shift between different states, pushing the system out of equilibirium.  For example, protein action plays a crucial role in the organization of the DNA inside the cell nucleus, modeled by a bead-spring polymer, in the form of stochastic crosslinking.  Despite these rapidly switching forces causing a constant state of disequilibrium, we observed in numerical simulations long-lived stable condensed clusters of beads consistent with experimental results, with the stochastic switching rate acting like an effective temperature.  Rapid switching produced low-temperature-like stable clusters, slow switching produced high-temperature-like amorphic arrangements, and intermediate switching times allowed for dynamic clusters with beads exchanging between clusters.  To explain the mechanism behind this emergent clustering behavior, we derive an effective thermal equilibrium that captures both the average force and fluctuations induced by the stochastically switching force, accurately predicting the mean transition time between stable configurations.   

Statistical Mechanics of Thermalized Odd Elastic Membranes

We are interested in studying the mechanical properties of thermalized 'odd' elastic membranes using statistical mechanics. Recently, generalizations of isotropic elastic structures to include active forces, specifically the 'odd' elastic forces were introduced by Colin Scheibner et al. Odd elastic 2-d membranes don't possess conservation of angular momentum and thus conservation of energy, thus rendering them to be systems without a Hamiltonian but possessing chiral forces. It was previously shown that for thermalized elastic membranes described by a Hamiltonian, fluctuations renormalize elastic constants, which become scale-dependent beyond a characteristic thermal length scale (a few nanometers for a real life example such as graphene at room temperature), beyond which the bending rigidity increases, while the in-plane elastic constants reduce with universal power law exponents. However, the fact that odd elastic membranes cannot be described by a Hamiltonian requires us to study this problem by means of the Langevin equation. Thus, dynamical effects will be accounted to better understand the role of these new chiral forces in thermalized thin elastic sheets. Both simulations and theory will be shown.   

Critical dynamics of the antiferromagnetic O(3) nonlinear sigma model with conserved total magnetization

We study the near-equilibrium critical dynamics of the O(3) nonlinear sigma model describing isotropic antiferromagnets with a conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen-De Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics to one-loop order. Since the static nonlinear sigma model is characterized by the (lower) critical dimension d_l = 2, whereas the reversible dynamical mode-coupling terms are governed by the upper critical dimension d_c= 4, a simultaneous dimensional ε expansion is not feasible, and the reversible critical dynamics for this model cannot be accessed at the static critical renormalization group fixed point. However, in the coexistence limit, we can perform the ε = 4 - d expansion near d_c, whereupon we recover the asymptotic dynamic exponents previously determined for the O(n)-symmetric Sasvári-Schwabl-Szépfalusy model in the ordered phase.   

Confidence bounds for the Jarzynski estimator

The Jarzynski equality relates the free energy differences between the equilibrium states of a system and the measurements of non-equilibrium work performed to move the system between the states. The determination of free energy differences using this relationship plays a crucial role in the study of physical, chemical, and biological systems at small scales. The Jarzynski equality computes the free energy differences using the mean of the exponentiated work and is thus asymptotic in nature. However, in practice, work can be measured only a finite number of times, leading to errors in the estimates. Studies that quantify this error are limited in number and scope. We provide non-restrictive and rigorous confidence bounds on the free energy difference estimates in this setting. These bounds are valid for a large class of work distributions and so are applicable for a broad variety of experiments that take the system far from equilibrium. Also, the bounds depend only on the finite samples of work measured in an experiment. This enables one to specify the largest error acceptable in the estimates and get a stopping criterion on the experimental trials. We include a Python-based toolbox that implements the bounds and showcase an empirical study that validates our claims.   

Stochastic thermodynamics of separation process in space and time: from kinetic proofreading to chromatography

In both living cells and chemical plants, the ability to recognize and discern molecules of similar properties is crucial. Separation of similar molecules can happen in both space and time. We model separation as random walks on graphs equipped with an inlet node and one or more outlet nodes. If the graphs represent chemical reaction networks, each node denotes an intermediate product of the reaction (i.e., a chemical-reaction state). If the graphs represent distillation or chromatography, each node corresponds to a physical location (spatial state). This work provides a unified description of various separations: kinetic proofreading as separation in the chemical space, distillation tower as a spatial separation, and chromatography as separation in the time domain. By performing kinetic Monte Carlo simulation of various designs of graphs, we can compare the performance of kinetic proofreading, chromatography, and some novel designs for accurate separation. Here we demonstrate that nonequilibrium cycles borrowed from the kinetic proofreading can significantly improve the separation performance of chromatography in the time domain.   

Every Raindrop is Exceptional

Rainfall from ice-free cumulus clouds requires collisions of very large numbers of microscopic droplets to create every raindrop, and the collision rate for the first few droplet coalescences is typically less than one per hour. The onset of rain showers can be surprisingly rapid, much faster than the mean time required for a single collision. The explanation is that every raindrop is the result of a sequence of exceptionally rare events, where the first few collisions happen unusually quickly.

The talk will discuss how large-deviation theory and extreme value statistics can give a quantitative description of rainfall, including recent results on the growth history of those 'lucky' microscopic droplets which grow to become raindrops.   

Spontaneous Chiral Symmetry Breaking in a Random, Driven Chemical System

Living systems have evolved to efficiently consume available energy sources using an elaborate circuitry of chemical reactions, but with a puzzling homochiral restriction in its chemical components. While autocatalysis is known to induce such chiral symmetry breaking, whether this might also arise in a more general class of non-autocatalytic chemical networks---by mere virtue of energy source exploitation---is a sensible yet underappreciated possibility. In this work, we examine this question within a model of randomly-generated complex chemical networks and show that chiral symmetry breaking may occur spontaneously and generically by harnessing energy sources from external environmental drives. Key to this transition are intrinsic fluctuations of achiral-to-chiral reactions and tight matching of system configurations to the environmental drive which, together, amplify and sustain diverged enantiomer distributions. The results thus demonstrate a generic mechanism in which energetic drives may give rise to homochirality in an otherwise totally symmetrical environment.   

Bona fide stochastic resonance without periodic forcing

We report on the synchronization of Brownian particles in nanoscale bistable potentials in the presence of correlated Poisson noise, with mean interval τ_P and correlation time τ_c, mimicking an active bath. The residence time distribution of the particle displays a series of peaks at integral multiples of τ_P. The peaks are maximal when the mean residence time τ_d matches the active noise time scales, 4τ_c≈τ_P≈τ_d/2, thereby demonstrating bona fide stochastic resonance in the absence of periodic force.  Additionally, we show that generic stochastic resonance under periodic forcing, known to degrade in strongly correlated continuous noise, is recovered by the discrete nonGaussian kicks.   

Ubiquitous power law intensity distributions in the self-excited nonlinear Hawkes processes

Self-excited mechanisms are prevalent in various complex systems, such as physical, seismic, neural, financial, and social systems, and one of the corresponding minimal models is the nonlinear Hawkes process. While this model has been popular and used for various data analyses of complex systems, its analytical properties have not been documented yet because of its non-Markovian and nonlinear characteristics. In this talk, we present its asymptotic solutions using the field master equation approach previously introduced by the authors. We first convert the original non-Markovian dynamics onto a high-dimensional Markovian field dynamics. By deriving the corresponding field master equation, the power law intensity distributions are found for a broad class of nonlinear Hawkes processes. Our work highlights the ubiquity of power laws in complex systems.