Session F24: Noise-Driven Dynamics in Far-From-Equilibrium Systems I

Climate variability: a manifestation of fluctuations in a nonequilibrium steady state

The climate system is forced by incoming solar radiation, is damped by outgoing long-wave radiation, and is, apart from time-dependent natural and anthropogenic forcing, approximately in a nonequilibrium steady state. The natural variability about the time-mean climate state takes the form of coherent, preferred, spatio-temporal patterns with names such as the El-Niño Southern Oscillation, the Madden-Julien Oscillation, the Atlantic Multidecadal Oscillation, and the Pacific Decadal Oscillation. These climate oscillations have large human impacts and their response to anthropogenic climate change is uncertain. Nonequilibrium steady states can be characterized by persistent currents in phase space and we interpret climate oscillations as the physical space manifestation of those phase space currents. We describe a new diagnostic for phase space currents, the phase space angular momentum, which describes the rotational flow of trajectories in phase space by analogy to the mass angular momentum of a fluid rotating in physical space. One advantage of the phase space angular momentum is that it can be readily calculated from an observed time series with no assumptions about an underlying model. We find that the phase space angular momenta in simple stochastic models of the El-Niño Southern Oscillation and the Madden-Julien Oscillation agree surprisingly well with that seen in observations of the climate system. We propose that the phase space angular momentum might be a useful general metric to describe fluctuations in nonequilibrium steady states.   

Critical Dynamics of Anisotropic Antiferromagnets in an External Field

We numerically investigate the non-equilibrium critical dynamics in three-dimensionalanisotropic antiferromagnetsin the presence of an external magnetic field. The phase space of this system exhibits two critical lines which meet at a bicritical point. In this system, the non-conserved components of staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. By employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, decay and aging collapse exponents, thus also verifying the dynamic critical exponent. We also probe the dynamic exponent of the model F critical line by investigating the system-size dependence of the characteristic spin wave frequencies near criticality. Furthermore, we investigate the aging scaling behavior of the slow order parameter and conserved field near the bicritical point.   

Current fluctuations in presence of time-periodic metabolic conditions

We address the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under time-varying metabolic conditions, modelled by a periodic modulation of the product concentration. Coarse-graining the original model to a minimal solvable one by means of a projection technique, we study the leading behavior of the time averaged current and its fluctuations using a large deviations approach. We show that there exist different regimes, depending on the kinetic rates, in which positive and negative amplitude resonant effects take place, and we provide interpretations for the role that these nonequilibrium effects can play in the metabolic network.
  

Large scale kinetic modeling of metabolic networks

Problems:
While the biochemistry of metabolism in many organisms is well studied, details of the metabolic dynamics are yet fully explored.

Unless the parameters of a vast number of enzyme-catalyzed reactions happened to fall into very special ranges, a kinetic model on a large metabolic network would fail to reach a steady state.

Acquiring adequate in vivo kinetic parameters experimentally has always been an obstacle.

Approach:
A stable metabolic network can be systematically established via a biologically/evolutionally motivated regulatory process.

May be understood via a landscape description of metabolism as a stochastic system, which draws enzymatic parameters towards stable phase spaces.

Allows explicit thermodynamics constraints on concentrations and optimal balance of efficiency vs viability (i.e. stability/fitness/robustness).

The strategy was applied sucessfully to the central metabolism of Methylobacterium extorquens AM1 and the secondary metabolism and metabolic switches in Streptomyces xiamenensis 318.   

Temperature interfaces in the Katz-Lebowitz-Spohn driven lattice gas

We explore the intriguing spatial patterns that emerge in a two-temperature Katz-Lebowitz-Spohn (KLS) model in two dimensions, a driven lattice gas with attractive nearest-neighbor interactions and periodic boundary conditions.The domain is split into two regions with hopping rates governed by different temperatures T > Tc and Tc, respectively, where Tc indicates the critical temperature for phase ordering. When the temperature boundaries are oriented transverse to the drive, the hotter region experiences an unexpected phase separation caused by the lower sustained current in the cooler region. The resulting density profiles in both hot and cold subsystems are similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, yet display marked fluctuation corrections. In contrast, when the temperature boundaries are oriented along the drive, the KLS dynamics is crucially determined by the choice of hopping rates across the temperature interfaces. In particular, when the latter break particle-hole symmetry, we observe particle influx from the cooler into the hotter region.   

Anomalous heating in a colloidal system: Observation of the inverse Mpemba effect

We present the first experimental observation of anomalous heating in colloidal systems, a phenomenon known as the inverse Mpemba effect. In particular, under certain conditions, we observe that an initially cold system heats up faster than an identical warm system when coupled to the same thermal bath. We study the effect in a system consisting of a Brownian particle in a tilted double-well potential set in an asymmetric domain. We also study the forward Mpemba effect, where an initially hot system cools faster than an identical warm system. We observe the forward effect for a wide range of temperatures and domain sizes (region in space explored by the particle). By controlling the relative sizes of the basins of attraction of the stable and metastable potential wells, we can provide a direct kinetic path between the hot initial state and the cold equilibrium. We then observe exponentially faster cooling. This is the first experimental evidence for the strong Mpemba effect.   

Decomposition of anomalous diffusion in generalized Lévy walks into its constitutive effects

Anomalous diffusion is observed in a variety of physical and social systems, including blinking quantum dots, animal locomotion, intra-day trades in financial markets and cold atoms in dissipative optical lattices. Generalized Lévy walks can be used to model their dynamics. We show that the anomalous diffusive behavior found in these systems can be decomposed into three fundamental constitutive causes. These causes, or effects, are related to ways that the Central Limit Theorem fails. The increments generated through the stochastic process can have either long-time correlations, infinite variance, or be non-stationary. Each of these properties can cause anomalous diffusion and is characterized by what is known as the Joseph, Noah and Moses effects, respectively. In generalized Lévy walks, a complex combination of these effects leads to the observed sub- and super-diffusive behaviors. We analytically calculate the scaling exponents determining each of the three constitutive effects and confirm the results with numerical simulations. The results satisfy a fundamental scaling relation between the exponents.   

A coupled two-species model for the pair contact process with diffusion

The contact process with diffusion (PCPD) defined by the pair reactions 2B→3B, 2B→0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies indicated that further coarse-graining of the model may be needed for its effective long-time, large-scale description. We introduce a coarse-grained two-species representation for the PCPD in which single particles B and particle pairs A are coupled according to the processes 2B→A, A→A+B, A→0, A→2B, with each type of particles diffusing independently. We employ Monte Carlo simulations in one, two, and three dimensions to demonstrate that this model consistently captures the pertinent features of the PCPD. In the inactive phase, A particles die out rapidly, effectively leaving the B species to undergo pure pair annihilation kinetics. At criticality, both A and B densities decay with similar exponents to those measured for the PCPD and display mean-field scaling above the critical dimension d_c=2. In one dimension, exponents for the B species obtained from seed simulations also agree well with previously reported ranges.   

Anomalous Diffusion with an Absorbing Wall

Fractional Brownian Motion and the Fractional Langevin Equation, random processes characterized by long-time power law correlations in the noise, are prototypical models for anomalous diffusion. We employ large scale Monte Carlo simulations to investigate these models in the presence of an absorbing wall. In the limit of vanishing correlations, our findings reproduce the well-known results for normal diffusion. In contrast, the interplay between the absorbing wall and the long-range power correlations leads to a singular probability density close to the wall. We compare our results to those of Fractional Brownian Motion [1] as well as the Fractional Langevin Equation [2] in the presence of a reflecting wall, and we discuss implications of our results.
[1] A.H.O Wada and T. Vojta, Phys. Rev. E 97, 020102 (2018)
[2] T. Vojta, S. Skinner, R. Metzler, arXix:1907.08188   

Diffusion in dynamic crowded spaces

Brownian motion in disordered media is now well understood in the case of immobile hard obstacles. In many practical applications, however, the space itself can be dynamic. An important example is transport inside the cell, a very crowded environment with obstacles of varying sizes and complicated shapes that are constantly being rearranged. This situation has received comparatively little attention. With the ever-increasing quality of microscopy techniques, allowing for the tracking of particles inside living cells, the need for a quantitative model is clear.

Here we propose an extension of commonly used "Swiss-cheese" models to include moving obstacles and study it with numerical simulations in one, two and three dimensions. The motion of our tracer particles is anomalous over many decades in time, before reaching a diffusive steady state with an effective diffusion constant that depends on the obstacle density and diffusivity. Moreover, we find that the scaling behaviour of the effective diffusivity, above and below a critical regime at the percolation point for void space, can be characterised by two critical exponents: the conductivity μ, also found in models with frozen obstacles, and a new exponent ψ that quantifies the effect of the obstacle diffusivity.   

Trajectories and transport characteristics of a Brownian particle in a 1D potential subject to bias.

We investigate one-dimensional driven, diffusive motion of a single Brownian particle moving through a periodic lattice potential and subject to a constant, uniform bias using a Langevin equation of motion. The model yields explicit trajectories with bias-dependent trapping, hopping, and linear response regimes at sufficiently low temperatures and the statistical behavior generated by an ensemble of trajectories are essentially those of an asymmetric simple exclusion process. Moreover, we find that, at low bias, the system exhibits a negative differential mobility, decreasing with applied bias, to a distinct local minimum in the hopping transport regime. In the context of the dynamical model, we argue the non-monotonic behavior of the transport coefficient can be explained by the role of friction as the particle passes through the minima in each well. Such a model may be employed to describe a wide variety of intriguing transport behaviors. As an example, we show that experimental data on the transition from static to kinetic friction through a plastic regime can be described by such a model.
  

Fluctuation theorem for geometric pumping processes

We derive an extended fluctuation theorem for an open quantum system coupled with two reservoirs under one-cycle modulation. We confirm that the geometric phase caused by the Berry-Sintisyn-Nemenman curvature in the parameter space generates non-Gaussian fluctuations. This non-Gaussianity is enhanced for the instantaneous fluctuation relation when the bias between the two reservoirs disappears.   

Stochastic Line Integrals as Metrics of Irreversibility and Heat Transfer

Stochastic line integrals provide a powerful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization of such integrals, the stochastic area, was recently introduced for linear systems and has been tested experimentally in coupled linear electrical circuits [1,2]. In this talk, we provide a framework for understanding general properties of stochastic line integrals and clarify their implementation for experiments and simulations as well as their utility as metrics for quantifying non-equilibrium behavior. Theoretical results are supported by numerical studies of an overdamped, two-dimensional mass-spring system driven out of equilibrium. In this case, the stochastic area can be concisely expressed in terms of a streamfunction the sign of which determines the orientation of probability current loops. Furthermore, the stream function allows one to analytically understand the dependence of stochastic area on key parameters such as the noise strength (equivalently temperature) for both nonlinear and linear springs.
[1] A. Ghanta, J. Neu, and S. Teitsworth, Phys. Rev. E 95, 032128 (2017).
[2] J. P. Gonzalez, J. Neu, and S. Teitsworth, Phy. Rev. E 99, 022143 (2019).