Nonequilibrium Behavior Research Articles

A Bayesian Level-k Model in n-Person Games

In standard models of iterative thinking, players choose a fixed rule level from a fixed rule hierarchy. Nonequilibrium behavior emerges when players do not perform enough thinking steps. Existing approaches, however, are inherently static. This paper introduces a Bayesian level-k model, in which level-0 players adjust their actions in response to historical game play, whereas higher-level thinkers update their beliefs on opponents’ rule levels and best respond with different rule levels over time. As a consequence, players choose a dynamic rule level (i.e., sophisticated learning) from a varying rule hierarchy (i.e., adaptive learning). We apply our model to existing experimental data on three distinct games: the p-beauty contest, Cournot oligopoly, and private-value auction. We find that both types of learning are significant in p-beauty contest games, but only adaptive learning is significant in the Cournot oligopoly, and only sophisticated learning is significant in the private-value auction. We conclude that it is useful to have a unified framework that incorporates both types of learning to explain dynamic choice behavior across different settings. This paper was accepted by Manel Baucells, decision analysis.

Harnessing currents of particles for spectroscopy in small-ring lattices with binary mixtures

We propose a method to probe ground states with distinct properties in binary mixtures trapped in small-ring lattices. The technique exploits the nonequilibrium particle current behavior generated by a nonadiabatic change of the interaction between the species of the binary mixture. The analysis of the current fluctuations in the Fourier space reveals a correspondence between the frequency peaks and specific particle-hole excitations, thereby performing a many-body spectroscopy of the ground state of the system. We show, for a small system, that the read out of the frequency spectrum can be used to detect essential features of a pair superfluid quantum phase. Remarkably, large frequency shifts of the spectral peaks provide an indication of relevant differences between ground states located very near in the parameter space. This spectral behavior allows establishing a criterium to determine in experiments changes in the properties of the ground state in small systems.

INFLUENCE OF STRUCTURAL DEFECTS ON NONEQUILIBRIUM CRITICAL BEHAVIOR OF THREE-DIMENSIONAL ANISOTROPIC HEISENBERG MODEL

The results of a Monte Carlo study of features of structural defects influence on nonequi-librium critical behavior of three-dimensional isotropic and anisotropic Heisenberg models are presented with their evolution from different initial states. It is shown that presence of defects changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type and evolution from both high-temperature and low-temperature initial states. Presence defects is relevant only for characteristics of nonequi-librium critical behavior of isotropic model with evolution from low-temperature initial state leading to superaging effects.

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier–Stokes equation

The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent motion is described by the stochastic Navier–Stokes equation with the random stirring force whose correlation function includes two terms that allow one to account both for a turbulent fluid and for a fluid in thermal equilibrium. The renormalization group analysis performed in the leading order of perturbation theory (one-loop approximation) reveals six possible types of scaling behaviour (universality classes). The most interesting values of the spatial dimension d = 2 and 3 correspond to the universality class of a pure turbulent advection where the nonlinearity of the Kardar-Parisi-Zhang model is irrelevant.

Boltzmann equation and hydrodynamic equations: their equilibrium and non-equilibrium behaviour.

This short article summarizes the key features of equilibrium and non-equilibrium aspects of Boltzmann and hydrodynamic equations. Under equilibrium, the Boltzmann equation generates uncorrelated random velocity that corresponds to k2 energy spectrum for the Euler equation. The latter spectrum is produced using initial configuration with many Fourier modes of equal amplitudes but with random phases. However, for a large-scale vortex as an initial condition, earlier simulations exhibit a combination of k-5/3 (in the inertial range) and k2 (for large wavenumbers) spectra, with the range of k2 spectrum increasing with time. These simulations demonstrate an approach to equilibrium or thermalization of Euler turbulence. In addition, they also show how initial velocity field plays an important role in determining the behaviour of the Euler equation. In non-equilibrium scenario, both Boltzmann and Navier-Stokes equations produce similar flow behaviour, for example, Kolmogorov's k-5/3 spectrum in the inertial range. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

High-Resolution Simulations for Aerogel Using Two-Phase Flow Equations and Godunov Methods

Aerogel is studied numerically using a one-dimensional two-phase flow equations system. A hyperbolic and conservative two-phase flow model is applied to a mixture of porous media containing nanofluids. The application of non-equilibrium mixture behavior between phases is adopted and promoted in this current investigation. By establishing mixture conservation balance laws, finite volume techniques using Godunov methods of centered type are extended to aerogel simulations. Numerical results are compared with other methods providing a remarkable agreement. The computed results demonstrate the key capabilities of this existing mixture model in the resolution of discontinuities in aerogel problems and more reliable than applying a sophisticated single-phase flows with complex property models.

Atypical behavior of collective modes in two-dimensional Fermi liquids

Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau’s Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c0. As a function of the usual dimensionless parameter s = ω/qvF, we find two peculiar results: first, for |s| > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for |s| < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ωp exhibiting a crossover to the zero sound mode.

Detecting the out-of-time-order correlations of dynamical quantum phase transitions in a solid-state quantum simulator

Quantum many-body systems in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, there still exist a lot of questions regarding how to understand the nonequilibrium dynamical behavior of quantum many-body systems, which are not accessible with the thermodynamic description. Experiments in quantum simulators are opening up a route toward the generation of quantum states beyond the equilibrium paradigm. As an example, in closed quantum many-body systems, dynamical quantum phase transitions act as phase transitions in time, with physical quantities becoming nonanalytic at a critical time, extending important principles such as universality to the nonequilibrium realm. Here, in a solid-state quantum simulator, we report the experimental detection of out-of-time-order correlators in the presence of nonequilibrium phase transitions with the transverse field Ising model, which are a central concept to quantify quantum information scrambling and quantum chaos. Through measuring the multiple quantum spectra, we eventually observe the buildup of quantum correlation. Further applications of this protocol could potentially enable studies of other exotic phenomena such as many-body localization and tests of the holographic duality between quantum and gravitational systems.

Effect of the Initial States, the Anisotropy, and Structural Defects on a Nonequilibrium Critical Behavior of the Three-Dimensional Heisenberg Model

A numerical Monte Carlo study has been performed on the influence of various initial states, easy-axis-type magnetic anisotropy, and structural defects on a nonequilibrium critical behavior of the classical three-dimensional Heisenberg model. An analysis of the time dependence of the magnetization and the autocorrelation function for the isotropic Heisenberg model shows substantial influence of the initial states on the relaxation of the magnetization and the aging effects in the behavior of the autocorrelation function, which are characterized by anomalous slowing down of the relaxation and correlation in the system as the waiting time increases. The study of the anisotropic Heisenberg model shows that the behavior of the magnetization and the autocorrelation function in a long-time regime is characterized by the critical exponents of the three-dimensional Ising model with a faster time decay of the autocorrelation function than that for the isotropic model. It has been revealed that the existence of structural defects in the case of the evolution of the system from the low-temperature initial state leads to an anomalously significant slowing down of the autocorrelation function. These features in the behavior of the autocorrelation function are characterized by the “superaging” effect with “superaging” exponent μ = 2.6(1) and related to the pinning of domain walls on structural defects during a nonequilibrium change in the domain structure of the system. In the case of evolution from the high-temperature initial state, the structural defects enhance the aging effect in the aging regime but their influence is irrelevant in the long-time regime.

Development of a stagnation streamline model for thermochemical nonequilibrium flow

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.

Do People Minimize Regret in Strategic Situations? A Level-k Comparison

Regret minimization and level-k reasoning have been proposed as alternative models for rationalizing non-equilibrium behavior in games. We provide a theoretical and experimental analysis of the relationship between these two models, a relationship that has been neglected by economists. Both theories predict the same behavior in a surprisingly large number of experimentally tested games. We identify conditions under which this happens and use them to design a series of games to separate minimax regret from level-1. The experimental test of these games and data from Costa-Gomes and Crawford (2006) reveal that no one systematically minimizes regret, casting doubt on minimax regret as a relevant explanation for behavior in strategic situations.

The algebraic geometry of perfect and sequential equilibrium: an extension

We extend the generic equivalence result of Blume and Zame (Econometrica 62:783–794, 1994) to a broader context of perfectly and sequentially rational strategic behavior (including equilibrium and nonequilibrium behavior) through a unifying solution concept of “mutually acceptable course of action” (MACA) proposed by Greenberg et al. (Econ Theory 40:91–112, 2009. https://doi.org/10.1007/s00199-008-0349-5 ). As a by-product, we show, in the affirmative, Dekel et al.’s (J Econ Theory 89:165–185, 1999) conjecture on the generic equivalence between the sequential and perfect versions of rationalizable self-confirming equilibrium.

A novel visualization approach for foamy oil non-equilibrium phase behavior study of solvent/live heavy oil systems

In this study, a novel visualization methodology to study solvent non-equilibrium exsolution behavior in heavy oil systems is proposed. A Hele-Shaw-like visual cell with adjustable aperture depth, has been designed to overcome the shortcomings of traditional apparatuses such as a hardly-visual PVT cell, or non-visual transfer cylinders. By eliminating the 3D nature of the traditional apparatuses, the true 2D bulk phase visual cell can directly visualize the interface evolution of foamy oil under pressure depletion. Totally, 6 sets of Constant Composition Expansion tests (CCE) were conducted with a CO2-C3H8-heavy live oil system. The effect of pressure depletion rates on solvent non-equilibrium exsolution behavior have been tested. Meanwhile, the initial volume fill-up percentage of live oil in the visual cell was also found to have an effect on foamy oil generation and endurability. This helps to define the appropriate volume of live oil to be saturated in PVT tests that aim to induce non-equilibrium. Through analyzing the deviation of liquid/vapor phase volume fraction from equilibrium state, non-equilibrium regimes of solvent exsolution were effectively found. The experimental design is also able to continuously capture the real-time solvent component exsolution sequence during pressure depletion. Numerical simulation of solvent non-equilibrium exsolution behavior has been conducted by a MATLAB-controlled reservoir simulator with real-time optimization. By dynamically adjusting the K value in the simulator, the total flashed vapor phase volume and the individual solvent component mass was history-matched. The achieved non-equilibrium K values were compared with equilibrium K values, and a delayed solvent exsolution was indicated.

Experimental and theoretical energetics of walking molecular motors under fluctuating environments

Molecular motors are nonequilibrium open systems that convert chemical energy to mechanical work. Their energetics are essential for various dynamic processes in cells, but largely remain unknown because fluctuations typically arising in small systems prevent investigation of the nonequilibrium behavior of the motors in terms of thermodynamics. Recently, Harada and Sasa proposed a novel equality to measure the dissipation of nonequilibrium small systems. By utilizing this equality, we have investigated the nonequilibrium energetics of the single-molecule walking motor kinesin-1. The dissipation from kinesin movement was measured through the motion of an attached probe particle and its response to external forces, indicating that large hidden dissipation exists. In this short review, aiming to readers who are not familiar with nonequilibrium physics, we briefly introduce the theoretical basis of the dissipation measurement as well as our recent experimental results and mathematical model analysis and discuss the physiological implications of the hidden dissipation in kinesin. In addition, further perspectives on the efficiency of motors are added by considering their actual working environment: living cells.

Dissipative Self-Assembly of Dynamic Multicompartmentalized Microsystems with Light-Responsive Behaviors

Summary Living cells are compartmentalized systems operating far from thermodynamic equilibrium and consume energy from the environment to carry out their functions. The construction of biomimetic synthetic compartments has both scientific and technological value. Despite many advances, the assembly of synthetic compartments that present nonequilibrium behaviors based on dissipative (or transient) self-assembly remains a grand challenge. Here, we describe the design and synthesis of multicompartmental systems with an active microstructure and complex behaviors. By including an artificial pathway for energy dissipation, we demonstrate the autonomous generation of active polymeric systems using a strategy based on polymerization-induced self-assembly (PISA), driven by chemical fuel. Remarkably, these self-organized synthetic systems exhibit a dynamic change in their multicompartmental structures when exposed to light. This work introduces a strategy toward the design and construction of synthetic compartments with a dynamic structure and also presents pathways to engineer materials with spatially controllable structures and functionalities.

Computational models for active matter

Active matter, which ranges from molecular motors to groups of animals, exists at different length scales and timescales, and various computational models have been proposed to describe and predict its behaviour. The diversity of the methods and the challenges in modelling active matter primarily originate from the out-of-equilibrium character, lack of detailed balance and of time-reversal symmetry, multiscale nature, nonlinearity and multibody interactions. Models exist for both dry active matter and active matter in fluids, and can be agent-based or continuum-level descriptions. They can be generic, emphasizing universal features, or detailed, capturing specific features. We compare various modelling approaches and numerical techniques to illuminate the innovations and challenges in understanding active matter. Active matter consists of energy-consuming units, which self-propel, exert forces on their neighbours and act collectively, resulting in emergent non-equilibrium behaviour. This Review surveys computational models that describe a wide range of active systems, from synthetic microswimmers to animal herds.

Gelation of Anisotropic Colloids with Short-Range Attraction

Gels are dilute connected networks that form solids at very low particle volume fraction with rich rheological properties. The kinetic process of gelation is central to understand the flow of complex fluids. Here, we report a simulation study of colloidal gelation formed by anisotropic colloids with attractive Lennard-Jones potential. These forces quasi-model the critical Casimir effect far from the critical solvent fluctuations acting on colloidal patches. By tuning the depths of the patch-to-patch particle interactions and the selected colloidal patches, we dynamically arrest the colloids to form gels. We find that thermal density fluctuation is the key factor to activate colloidal cluster space spanning: the balance between clustering and break-up mechanism plays a major role in the gelation process of anisotropic systems. These results offer new opportunities for studying the structural modifications of colloidal gels formed by anisotropic particles, and shed light on non-equilibrium behavior of anisotropic colloidal building blocks.

Sorption and transport behavior of zinc in the soil; Implications for stormwater management

Long-term leaching of accumulated heavy metals from the filter media of stormwater infiltration systems into groundwater, and its subsequent movement into receiving waters, is a concern for stormwater management in urban landscapes. This study provides a critical understanding of the fate of heavy metals, in particular zinc, in the subsurface to improve stormwater management. We studied the sorption behavior of zinc during its transport in soil using batch and column experiments. The use of sorption parameters from batch studies failed to suitably describe the zinc breakthrough curves simulated with the HYDRUS-1D model. While a sharp breakthrough curve front was expected due to the nonlinear nature of the batch sorption isotherms, we observed a more dispersed asymmetrical front in the columns. This demonstrates the existence of chemical non-equilibrium sorption during zinc transport. Conversely, no asymmetry was observed in the conservative tracer (chloride) breakthrough curve, suggesting that there is no physical non-equilibrium component. We conclude that (1) batch tests overpredict the transport behavior of zinc in the soil, (2) column tests better approximate non-equilibrium sorption behavior of zinc during its transport through the soil, and therefore should be conducted to better predict the contaminant transport behavior in the surrounding soils, and that (3) the sorption behavior of zinc transport is predominantly influenced by chemical sorption-related than physical transport-related mechanism. The outcomes of this research suggest that stormwater managers should consider the heterogeneity of surrounding soil between the infiltration systems and receiving waters and its impact on the transport of heavy metals when designing stormwater infiltration systems. Otherwise, they run the risk of not delivering the desired restoration of urban ecosystems.

Temporal relaxation of gapped many-body quantum systems

Typicality of the orthogonal dynamics (TOD) is established as a generic feature of temporal relaxation processes in isolated many-body quantum systems. The basic idea in the simplest case is that the transient non-equilibrium behavior is mainly governed by the component of the time-evolved system state parallel to the initial state, while the orthogonal component appears as equilibrated right from the beginning. The main emphasis is laid on the largely unexplored and particularly challenging case that one energy level exhibits a much larger population than all the others. Important examples are gapped many-body systems at low energies, for instance due to a quantum quench. A general analytical prediction is derived and is found to compare very well with various numerically exact results.

Optical "Blinking" Triggered by Collisions of Single Supramolecular Assemblies of Amphiphilic Molecules with Interfaces of Liquid Crystals.

We report that incubation of aqueous dispersions of supramolecular assemblies formed by synthetic alkyl triazole-based amphiphiles against interfaces of thermotropic liquid crystals (LCs; 4-cyano-4'-pentylbiphenyl) triggers spatially localized (micrometer-scale) and transient (subsecond) flashes of light to be transmitted through the LC. Analysis of the spatiotemporal response of the LC supports our proposal that each optical "blinking" event results from collision of a single supramolecular assembly with the LC interface. Particle tracking at the LC interface confirmed that collision and subsequent spreading of amphiphiles at the interface generates a surface pressure-driven interfacial flow (Marangoni flow) that causes transient reorientation of LC and generation of a bright optical flash between crossed polarizers. We also found that dispersions of phospholipid vesicles cause "blinks". When using vesicles formed from 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), we measured the frequency of blinking to decrease proportionally with the number density of vesicles in the aqueous phase, consistent with single vesicle events, with the lifetime of each blink dependent on vesicle size (800 ± 80 nm to 150 ± 30 nm). For 100 μM of DLPC, we measured vesicles with a diameter of 940 ± 290 nm to generate 47 ± 9 blinks min-1 mm-2, revealing that the fraction of vesicle collisions resulting in fusion with the LC interface is ∼10-3. Overall, the results in this paper unmask new nonequilibrium behaviors of amphiphiles at LC interfaces, and provide fresh approaches for exploring the dynamic interactions of supramolecular assemblies of amphiphiles with fluid interfaces at the single-event level.