Nonequilibrium Phase Research Articles

Dynamical theory for adaptive systems

Abstract The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former’s dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach à la Martin–Siggia–Rose-De Dominicis–Janssen to analyse non-equilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness.

Active fluctuations of axoneme oscillations scale with number of dynein motors

Fluxes of energy generate active forces in living matter, yet also active fluctuations. As a canonical example, collections of molecular motors exhibit spontaneous oscillations with frequency jitter caused by nonequilibrium phase fluctuations. We investigate phase fluctuations in reactivated Chlamydomonas reinhardtii axonemes, which are accessible to direct manipulation. We quantify the precision of axonemal oscillations after controlled chemical removal of dynein motors, providing an experimental test for the theory prediction that the quality factor of motor oscillations should increase with motor number. Our quantification reveals specialized roles of inner and outer arm dynein motors. This supports a model in which inner dyneins serve as master pace-makers, to which outer arm dyneins become entrained, consistent with recent insight provided by structural biology.

Tunable disorder on the S-state majority-voter model.

We investigate the nonequilibrium phase transition in the S-state majority-vote model for S=2,3, and 4. Each site, k, is characterized by a distinct noise threshold, qk, which indicates its resistance to adopting the majority state of its Nv nearest neighbors. Precisely, this noise threshold is governed by a hyperbolic distribution, P(k)∼1/k, bounded within the limits e-α/2<qk<1/2. Here, the parameter α plays a pivotal role as it determines the extent of disorder in the system through the spread of the threshold distribution. Through Monte Carlo simulations and finite-size scaling analyses on regular square lattices, we deduced that the model undergoes a continuous order-disorder phase transition at a specific α=αc. Interestingly, the critical threshold exhibits a power-law decay, αc∼Nv-δ, as the number Nv of neighboring sites increases. From the least square fits to the data sets results in δ=0.65±0.01 for S=2, δ=0.92±0.01 for S=3, and δ=0.93±0.01 for S=4. Furthermore, the critical exponents β/ν and γ/ν are consistent with those found in the S-state Potts model.

Effect of non-equilibrium phase transition on the aero-thermodynamic performance of supercritical carbon dioxide compressors

Phase transition is a prominent issue for the supercritical CO2 compressors operating near the critical region. The non-equilibrium behavior of phase transition makes it difficult to accurately predict performance under these conditions. A non-equilibrium phase transition model is proposed to analyze the aero-thermodynamic performance of supercritical CO2 centrifugal compressors with different inlet conditions. The model examines phase change characteristics and compressor performance under variable operating conditions. The results indicate that this model can effectively predict the aero-thermodynamic performance of compressor near critical conditions, with an average error of less than 2% in the performance curves. The inconsistency between low-temperature and low-pressure regions, along with the increase in liquid phase volume, are typical characteristics of non-equilibrium phase transition in supercritical CO2 compressors. The non-equilibrium effect of phase transition can reduce the leakage loss at high flow rates, but also increases the likelihood of stall at low flow rates. Furthermore, the concept of “non-equilibrium degree” (NED) is introduced to quantify these effects. When NED exceeds 0.2, the isentropic efficiency of the compressor decreases by 15.1% compared to its maximum efficiency. Designing inlet conditions for supercritical CO2 compressors with NED below 0.1 is more suitable because it has a larger inlet flowrate and higher efficiency.

CFD unified approach under Eulerian-Lagrangian framework for methanol and gasoline direct injection sprays in evaporative and flash boiling conditions

Innovative synthetic fuels for advanced propulsion systems, such as methanol and ammonia, and synthetic blended fuels (E00, E10, and E30), known for their high volatility, are often injected directly into combustion chambers. It follows that Eulerian-Lagrangian spray models need to accurately capture the spray collapse as a consequence of flash boiling onset and be capable of proficiently handling the preferential evaporation of multi-component fuels in evaporative scenarios.So, we performed the assessment of an Eulerian-Lagrangian CFD code for simulating methanol and E00 gasoline blend sprays in both early and late injection conditions involving flash boiling conditions and preferential evaporation. The adoption of an effervescent breakup model and of a non-equilibrium phase transition model for the discrete phase allows the adoption of a setup that is almost completely free from specific constant tuning, especially for what concerns the breakup model. We validated the simulations using experimental PLV maps of methanol and E00 sprays issued from the ECN Spray M injector. The results highlight a significantly different morphology of the methanol spray compared to the E00 one under late injection conditions. Under stratified combustion, low-volatile fuels are likely to be ignited first, and the flame propagates toward the high-volatile fuels. The spray collapse was also correctly reproduced, inducing the presence of a low-pressure zone and modifying the spray morphology.

Anomalous Directed Percolation on a Dynamic Network Using Rydberg Facilitation.

The facilitation of Rydberg excitations in a gas of atoms provides an ideal model system to study epidemic evolution on (dynamic) networks and self-organization of complex systems to the critical point of a nonequilibrium phase transition. Using MonteCarlo simulations and a machine learning algorithm we show that the universality class of this phase transition can be tuned but is robust against decay inherent to the self-organization process. The classes include directed percolation (DP), the most common class in short-range spreading models, and mean-field (MF) behavior, but also different types of anomalous directed percolation (ADP), characterized by rare long-range excitation processes. In a frozen gas, ground state atoms that can facilitate each other form a static network, for which we predict DP universality. With atomic motion the network becomes dynamic by long-range (Lévy-flight type) excitations. This leads to continuously varying critical exponents, varying smoothly between DP and MF values, corresponding to the ADP universality class. These findings also explain the recently observed critical exponent of Rydberg facilitation in an ultracold gas experiment [Helmrich etal., Nature (London) 577, 481 (2020)NATUAS0028-083610.1038/s41586-019-1908-6], which was in between DP and MF values.

Collective behavior of active filaments with homogeneous and heterogeneous stiffness.

The collective dynamics of active biopolymers is crucial for many processes in life, such as cellular motility, intracellular transport, and division. Recent experiments revealed fascinating self-organized patterns of diverse active filaments, while an explicit parameter control strategy remains an open problem. Moreover, theoretical studies so far mostly dealt with active chains with uniform stiffness, which are inadequate in describing the more complicated class of polymers with varying stiffness along the backbone. Here, using Langevin dynamics simulations, we investigate the collective behavior of active chains with homogeneous and heterogeneous stiffness in a comparative manner. We map a detailed non-equilibrium phase diagram in activity and stiffness parameter space. A wide range of phase states, including melt, cluster, spiral, polar, and vortex, are demonstrated. The appropriate parameter combination for large-scale polar and vortex formation is identified. In addition, we find that stiffness heterogeneity can substantially modulate the phase behaviors of the system. It has an evident destructive effect on the long-ranged polar structure but benefits the stability of the vortex pattern. Intriguingly, we unravel a novel polar-vortex transition in both homogeneous and heterogeneous systems, which is closely related to the local alignment mechanism. Overall, we achieve new insights into how the interplay among activity, stiffness, and heterogeneity affects the collective dynamics of active filament systems.

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties.

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

Long-lived topological time-crystalline order on a quantum processor

Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.

Polyoxometalate Reinforced Perovskite Phase for High-Performance Perovskite Photovoltaics.

Ionic hybrid perovskites face challenges in maintaining their structural stability against non-equilibrium phase degradation, therefore, it is essential to develop effective ways to reinforce their corner-shared [PbI6]4- octahedral units. To strengthen structural stability, redox-active functional polyoxometalates (POMs) are developed and incorporated into perovskite solar cells (PSCs) to form a robust polyoxometalates/perovskite interlayer for stabilizing the perovskite phase. This approach offers several advantages: 1) promotes the formation of an interfacial connecting layer to passivate interfacial defects in addition to stabilize the [PbI6]4- units through exchanged ammonium cations in POMs with perovskites; 2) facilitates continuous structural repairing of Pb0- and I0-rich defects in the [PbI6]4- unit through redox electron shuttling of the electroactive metal ions in POMs; 3) provides guidance for selecting suitable redox mediators based on the kinetic studies of POM's effectiveness in reacting with targeted defects. The POM-reinforced device maintains 97.2% of its initial PCE after 1500 h of shelf-life test at 65°C, while also enhancing the long-term operational stability. Additionally, this approach can be generally applicable across scalable sizes and various bandgap perovskites in devices, showing the promise of using functional POMs to enhance perovskite photovoltaic performance.

Applicability of Mean-Field Theory for Time-Dependent Open Quantum Systems with Infinite-Range Interactions.

Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance, and nuclear physics. From a theoretical viewpoint, these systems are appealing since they can be efficiently studied with numerics, and in the thermodynamic limit are expected to be governed by mean-field equations of motion. Over the past years the capabilities to experimentally create long-range interacting systems have dramatically improved permitting their control in space and time. This allows us to induce and explore a plethora of nonequilibrium dynamical phases, including time crystals and even chaotic regimes. However, establishing the emergence of these phases from numerical simulations turns out to be surprisingly challenging. This difficulty led to the assertion that mean-field theory may not be applicable to time-dependent infinite-range interacting systems. Here, we rigorously prove that mean-field theory in fact exactly captures their dynamics, in the thermodynamic limit. We further provide bounds for finite-size effects and their dependence on the evolution time.

Should We Conserve Entropy or Energy when Computing CAPE with Mixed-Phase Precipitation Physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from nonequilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution-dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1%–3% as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 and 250 m using explicit first-order and second-order integration schemes, respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast to energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution, whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency. Significance Statement Convective available potential energy (CAPE) is a measure of instability in the atmosphere that helps forecasters and researchers understand when and where thunderstorms will form. The purpose of this article is to identify the most efficient and accurate methods for computing CAPE. Two methods are considered here, one that relates to the entropy (a measure of thermodynamic disorder) of an air parcel and one that relates to the energy of an air parcel. Results indicate that the entropy method is most accurate and insensitive to the resolution of the data used for the calculation (which can vary considerably), whereas the energy method uses the least computation time.

Antiscreening and Nonequilibrium Layer Electric Phases in Graphene Multilayers.

Screening is a ubiquitous phenomenon through which the polarization of bound or mobile charges tends to reduce the strengths of electric fields inside materials. Here, we show how photoexcitation can be used as a knob to transform conventional out-of-plane screening into antiscreening-the amplification of electric fields-in multilayer graphene. We find that, by varying the photoexcitation intensity, multiple nonequilibrium screening regimes can be accessed, including near-zero screening, antiscreening, and overscreening (reversing electric fields). Strikingly, at modest continuous wave photoexcitation intensities, the nonequilibrium polarization states become multistable, hosting light-induced ferroelectriclike steady states with nonvanishing out-of-plane polarization (and band gaps) even in the absence of an externally applied displacement field in nominally inversion symmetric stacks. This rich phenomenology reveals a novel paradigm of dynamical quantum matter that we expect will enable a variety of nonequilibrium broken symmetry phases.

Study on the room temperature compression deformation mechanism and microstructural evolution of Mg-Gd-Y-Zr alloy

This study explores the dynamic impact deformation mechanisms of Mg-Gd-Y-Zr alloys, specifically focusing on the influence of varying Gd content. Using metallographic observation, SEM, EDS, XRD, EBSD, and TEM, along with hardness and room-temperature compression tests, the research investigates the effects of Gd content on the microstructure, mechanical properties, and deformation behaviors of as-cast Mg-(x)Gd-3Y-0.5Zr (x = 6.5/7.5/8.5) alloys.The results show that increasing Gd content reduces grain size and increases the volume fraction of the non-equilibrium eutectic phase Mg24(Gd,Y)5, though with smaller phase dimensions. These alloys exhibit excellent compressive properties at room temperature, with the highest compression deformation rate of 27.8 % observed at 6.5 % Gd and the maximum compressive strength of 401 MPa recorded at 8.5 % Gd, surpassing some high-Gd-content cast and extruded alloys.At lower Gd content, basal slip and tensile twinning are the primary deformation mechanisms. As Gd content increases, these mechanisms evolve to include prismatic slip and compressive twinning. The fracture mode transitions from predominantly ductile to a combination of ductile and brittle features, with an increase in brittle cleavage at higher Gd levels.

Nonequilibrium phase transitions in a 2D ferromagnetic spins with effective interactions

Nonequilibrium phase transitions in a 2D ferromagnetic spins with effective interactions

A comprehensive neural network study of the non-equilibrium phase transition of the two-dimensional Ising model on the square lattice

A comprehensive neural network study of the non-equilibrium phase transition of the two-dimensional Ising model on the square lattice

Probing spin hydrodynamics on a superconducting quantum simulator

Characterizing the nature of hydrodynamical transport properties in quantum dynamics provides valuable insights into the fundamental understanding of exotic non-equilibrium phases of matter. Experimentally simulating infinite-temperature transport on large-scale complex quantum systems is of considerable interest. Here, using a controllable and coherent superconducting quantum simulator, we experimentally realize the analog quantum circuit, which can efficiently prepare the Haar-random states, and probe spin transport at infinite temperature. We observe diffusive spin transport during the unitary evolution of the ladder-type quantum simulator with ergodic dynamics. Moreover, we explore the transport properties of the systems subjected to strong disorder or a tilted potential, revealing signatures of anomalous subdiffusion in accompany with the breakdown of thermalization. Our work demonstrates a scalable method of probing infinite-temperature spin transport on analog quantum simulators, which paves the way to study other intriguing out-of-equilibrium phenomena from the perspective of transport.

Origins of complexity in the rheology of Soft Earth suspensions

When wet soil becomes fully saturated by intense rainfall, or is shaken by an earthquake, it may fluidize catastrophically. Sand-rich slurries are treated as granular suspensions, where the failure is related to an unjamming transition, and friction is controlled by particle concentration and pore pressure. Mud flows are modeled as gels, where yielding and shear-thinning behaviors arise from inter-particle attraction and clustering. Here we show that the full range of complex flow behaviors previously reported for natural debris flows can be reproduced with three ingredients: water, silica sand, and kaolin clay. Going from sand-rich to clay-rich suspensions, we observe continuous transition from brittle (Coulomb-like) to ductile (plastic) yielding. We propose a general constitutive relation for soil suspensions, with a particle rearrangement time that is controlled by yield stress and jamming distance. Our experimental results are supported by models for amorphous solids, suggesting that the paradigm of non-equilibrium phase transitions can help us understand and predict the complex behaviors of Soft Earth suspensions.

Controlled Defective Engineering on CuIr Catalyst Promotes Nitrate Selective Reduction to Ammonia.

Electrochemical nitrate reduction reaction (NO3-RR) is a promising low-carbon and environmentally friendly approach for the production of ammonia (NH3). Herein, we develop a high-temperature quenched copper (Cu) catalyst with the aim of inducing nonequilibrium phase transformation, revealing the multiple defects (distortion, dislocations, vacancies, etc.) presented in Cu, which lead to low overpotential for NO3-RR and high efficiency for NH3 production. Further loading a low content of iridium (Ir) species on the Cu surface improves the reactivity and ammonia selectivity. The resultant CuIr electrode exhibits a Faradaic efficiency of 93% and a record yield of 6.01 mmol h-1 cm-2 at -0.22 VRHE exceeding those of state-of-the-art NO3-RR catalysts. Detailed investigations have demonstrated that the synergistic effect between multiple defects and Ir decoration effectively regulate the d-band center of copper, change the adsorption state of the catalyst surface, and promote the adsorption and reduction of intermediates and reactants. The strong H* adsorption ability of the Ir element provides more active hydrogen for the generation of ammonia, promoting the reduction of nitrate to NH3.

Dynamics of drug trafficking: Results from a simple compartmental model

In this work we propose a simple model for the emergence of drug dealers. For this purpose, we built a compartmental model considering four subpopulations, namely susceptibles, passive supporters, drug dealers and arrested drug dealers. The target is to study the influence of the passive supporters on the long-time prevalence of drug dealers. Passive supporters are people who are passively consenting to the drug trafficking cause. First we consider the model on a fully connected network, in such a way that we can write a rate equation for each subpopulation. Our analytical and numerical results show that the emergence of drug dealers is a consequence of the rapid increase in the number of passive supporters. Such increase is associated with a nonequilibrium active-absorbing phase transition. After that, we consider the model on a two-dimensional square lattice, in order to compare the results in the presence of a simple social network with the previous results. The Monte Carlo simulation results suggest a similar behavior in comparison with the fully connected network case, but the location of the critical point of the transition is distinct, due to the neighbors’ correlations introduced by the presence of the lattice.