Nonequilibrium Features Research Articles

On the nonequilibrium dynamics of gravitational algebras

Abstract We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type II ∞ von Neumann algebra. We discuss how this algebra can be coupled to the algebra of observable of an infinite reservoir within the canonical ensemble, aiming to induce nonequilibrium dynamics. The resulting dynamics can lead the system towards a nonequilibrium steady state which can be characterized through modular theory. Within this framework we address the definition of entropy production and its relationship to relative entropy, alongside exploring other applications.

Alpha–Proton Differential Flow of a Coronal Mass Ejection at 15 Solar Radii

Alpha–proton differential flow (V α p ) of coronal mass ejections (CMEs) and solar wind from the Sun to 1 au and beyond could influence the instantaneous correspondence of absolute abundances of alpha particles (He2+/H+) between the solar corona and interplanetary space as the abundance of a coronal source can vary with time. Previous studies based on Ulysses and Helios showed that V α p is negligible within CMEs from 5 to 0.3 au, similar to slow solar wind (<400 km s−1). However, recent new observations using Parker Solar Probe (PSP) revealed that the V α p of slow wind increases to ∼60 km s−1 inside 0.1 au. It is important to answer whether the V α p of CMEs exhibits similar behavior near the Sun. In this Letter, we report the V α p of a CME measured by PSP at ∼15 R ⊙ for the first time, which demonstrates that the V α p of CMEs is obvious and complex inside 0.1 au while keeping lower than the local Alfvén speed. A very interesting point is that the same one CME duration can be divided into A and B intervals clearly with Coulomb number below and beyond 0.5, respectively. The means of V α p and alpha-to-proton temperature ratios of interval A (B) is 96.52 (21.96) km s−1 and 7.65 (2.23), respectively. This directly illustrates that Coulomb collisions play an important role in reducing the nonequilibrium features of CMEs. Our study indicates that the absolute elemental abundances of CMEs also might vary during their propagation.

Effects of Particle Migration on the Relaxation of Shock Wave Collisions.

The non-equilibrium characteristics during the shock relaxation process hold a foundational position in various fields. In contrast to the propagation of a single shock wave, the collision process of two shock waves exhibits distinct non-equilibrium features. Employing non-equilibrium molecular dynamics, we simulated the collision of ultra-strong shock waves in a classical gas system, investigating the relationship between equilibrium relaxation time and shock intensity. Tracking the spatial migration of microscopic particles in the shock collision region during the relaxation process, we observed a significant contribution of particle migration to the average energy changes during relaxation. The discussion on particle migration provides a valuable new perspective for understanding the microscopic mechanisms of the relaxation process.

Study on The Evaluation of Eco-Economic Efficiency in The Yangtze River Economic Zone

Eco-economic efficiency is of tremendous significance to the coordinated development of ecological environment and economy. This study uses the super-SBM model to assess the Yangtze River Economic Belt’s ecological and economic performance from 2011 to 2020. The Malmquist index approach is then used to dynamically analyze the total factor productivity. The findings indicate that there is a non-equilibrium feature in space and that the eco-economic efficiency of the Yangtze River Economic Zone as a whole exhibits a fluctuating rising trend. A downstream &gt; midstream &gt; upstream pattern is shown. Based on the dynamic Malmquist index and its decomposition, the Yangtze River Economic Zone’s total factor productivity has a robust upward tendency. The primary cause of the shift in total factor productivity is technological advancement.

Spatial confinement affects the heterogeneity and interactions between shoaling fish

Living objects are able to consume chemical energy and process information independently from others. However, living objects can coordinate to form ordered groups such as schools of fish. This work considers these complex groups as living materials and presents imaging-based experiments of laboratory schools of fish to understand how activity, which is a non-equilibrium feature, affects the structure and dynamics of a group. We use spatial confinement to control the motion and structure of fish within quasi-2D shoals of fish and use image analysis techniques to make quantitative observations of the structures, their spatial heterogeneity, and their temporal fluctuations. Furthermore, we utilize Monte Carlo simulations to replicate the experimentally observed data which provides insight into the effective interactions between fish and confirms the presence of a confinement-based behavioral preference transition. In addition, unlike in short-range interacting systems, here structural heterogeneity and dynamic activities are positively correlated as a result of complex interplay between spatial arrangement and behavioral dynamics in fish collectives.

Causality-Driven Intra-class Non-equilibrium Label-Specific Features Learning

In multi-label learning, label-specific feature learning can effectively avoid some ineffectual features that interfere with the classification performance of the model. However, most of the existing label-specific feature learning algorithms improve the performance of the model for classification by constraining the solution space through label correlation. The non-equilibrium of the label distribution not only leads to some spurious correlations mixed in with the calculated label correlations but also diminishes the performance of the classification model. Causal learning can improve the classification performance and robustness of the model by capturing real causal relationships from limited data. Based on this, this paper proposes a causality-driven intra-class non-equilibrium label-specific features learning, named CNSF. Firstly, the causal relationship between the labels is learned by the Peter-Clark algorithm. Secondly, the label density of all instances is calculated by the intra-class non-equilibrium method, which is used to relieve the non-equilibrium distribution of original labels. Then, the correlation of the density matrix is calculated using cosine similarity and combined with causality to construct the causal density correlation matrix, to solve the problem of spurious correlation mixed in the label correlation obtained by traditional methods. Finally, the causal density correlation matrix is used to induce label-specific feature learning. Compared with eight state-of-the-art multi-label algorithms on thirteen datasets, the experimental results prove the reasonability and effectiveness of the algorithms in this paper.

Discrete modelling of continuous dynamic recrystallisation by modified Metropolis algorithm

Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains challenging for the existing modelling approaches based on continuum mathematics because they do not capture important local interactions between microstructure elements and spatial inhomogeneities in plastic strain. An effective discrete method for simulating CDRX is developed in this work. It employs algebraic topology, graph theory and statistical physics tools to represent an evolution of grain boundary networks as a sequence of conversions between low-angle grain boundaries (LAGBs) and high-angle grain boundaries (HAGBs) governed by the principle of minimal energy increase, similar to the well-known Ising model. The energy is minimised by a modified Metropolis algorithm. The model is used to predict the equilibrium fractions of HAGBs in several SPD-processed copper alloys. The analysis captures non-equilibrium features of the transitions from sub-grain structures to new HAGB-dominated grain structures and provides estimations of critical values for HAGB fractions and accumulated strain at these transitions.

Microstructural evolution of rapidly solidified hypoeutectic Al[sbnd]10Cu alloy during non-isothermal annealing transients induced by nano-second laser pulses

The evolution of characteristic nonequilibrium features presenting in morphologically distinct regions of rapid solidification (RS) microstructures in a hypoeutectic Al10Cu (atomic %) in response to non-isothermal annealing transients has been studied by transmission electron microscopy (TEM). The capabilities of the Movie-Mode Dynamic TEM (MM-DTEM) instrument were used to expose select regions of the RS microstructure to sequences of rapid heating and cooling transients induced by nanosecond laser pulses while permitting in-situ observation. Partial melting, microstructural scale coarsening, morphological changes of the nonequilibrium features in the multi-phase RS microstructure, and solid-state phase transformation were observed. Heterogeneous nucleation of nanoscale θ-Al2Cu phase involved metastable supersaturated α-Al and the θ'-Al2Cu phases, establishing different sets of orientation relationships for the stable θ-Al2Cu and α-Al phases. Replacement of banded morphology grains that formed under conditions driven farthest from equilibrium by an equiaxed nanocrystalline structure comprised of α-Al phase, the primary solidification product, and an intergranular network of Al2Cu crystals has been attributed to local remelting. The experimental approach explored here permitted discovery of mechanistic details of location-specific transformation pathways activated in the multi-phase RS microstructure of hypoeutectic AlCu during subsequent nonisothermal transients.

Laser-induced heating for the experimental study of critical Casimir forces with optical trapping

Critical Casimir interactions represent a perfect example of bath-induced forces at mesoscales. These forces may have a relevant role in the living systems as well as a role in the design of nanomachines fueled by environmental fluctuations. Since the thermal fluctuations are enhanced in the vicinity of a demixing point of a second-order phase transition, we can modulate the magnitude and range of these Casimir-like forces by slight changes in the temperature. Here, we consider two optical trapped colloidal beads inside a binary mixture. The Casimir interaction is controlled by warming the mixture by laser-induced heating, whose local application ensures high reproducibility. Once this two-particle system is warmed, the critical behavior of different observables allows the system to become its self-thermometer. We use this experimental scheme for analyzing the energetics of a critical colloidal system under a non-equilibrium-driven protocol. We quantify how the injected work can be dissipated to the environment as heat or stored as free energy. Indeed, our system allows us to use the fluctuation theorems framework for analyzing the performance of this critically driven toy model. Our work paves the way for future experimental studies on the non-equilibrium features of bath-induced forces and the design of critically driven nanosystems.

Microscopic theory, analysis, and interpretation of conductance histograms in molecular junctions

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here we develop a microscopic theory for the conductance histogram by merging the theory of force-spectroscopy with molecular conductance. The procedure yields analytical equations that accurately fit the conductance histogram of a wide range of molecular junctions and augments the information content that can be extracted from them. Our formulation captures contributions to the conductance dispersion due to conductance changes during the mechanical elongation inherent to the experiments. In turn, the histogram shape is determined by the non-equilibrium stochastic features of junction rupture and formation. The microscopic parameters in the theory capture the junction’s electromechanical properties and can be isolated from separate conductance and rupture force (or junction-lifetime) measurements. The predicted behavior can be used to test the range of validity of the theory, understand the conductance histograms, design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

Probing effects of solute trapping on the mechanical properties of α-Al in rapidly solidified hypoeutectic Al-10at.%Cu after surface laser melting

After scanned laser surface remelting the resultant rapid solidification microstructures of multicomponent alloys exhibit morphological gradients, with scale refinement and non-equilibrium features, including non-equilibrium solute trapping, which are associated with property changes. Combinations of site-specific mechanical property measurements by nano-indentation and microstructural analyses by electron microscopy have been used to determine microstructure-property relationships for the characteristic features of the rapid solidification microstructure of a hypo-eutectic Al–Cu alloy containing 10 atom percent Cu. A microstructure gradient developed as the solidification rate increased monotonically during the re-solidification process. For a laser scan velocity of 3 mm/s most of the rapid solidification microstructure is comprised of micrometer scale refined dendritic cells of α-Al(Cu) and nanometer scale refined intercellular θ-Al2Cu phase or eutectic. The cellular α-Al(Cu) constituent consistently showed Cu-solute supersaturation and a 36 % hardness increase relative to the as-cast state. The eutectic microconstituent exhibited increases in hardness that correlated quantitatively with the increasing lamellar spacing refinement obtaining for increasing solidification rate. The possible contributions from precipitation, solute and grain-size strengthening mechanisms to the hardness increase in the α-Al(Cu) cells have been assessed. The hardness increase of the α-Al(Cu) cells was attributed to a combination of solute and grain size strengthening.

Statistical features of systems driven by non-Gaussian processes: theory & practice

Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here we consider a class of Markov processes described by Langevin equations driven by a mixture of Gaussian and Poissonian noises, focusing on their non-equilibrium properties. In particular, we prove that detailed balance does not hold even when correlation functions are symmetric under time reversal. In such cases, a breakdown of the time reversal symmetry can be highlighted by considering higher order correlation functions. Furthermore, the entropy production may be different from zero even for vanishing currents. We provide analytical expressions for the average entropy production rate in several cases. We also introduce a scale dependent estimate for entropy production, suitable for inference from experimental signals. The empirical entropy production allows us to discuss the role of spatial and temporal resolutions in characterizing non-equilibrium features. Finally, we revisit the Brownian gyrator introducing an additional Poissonian noise showing that it behaves as a two dimensional linear ratchet. It has also the property that when Onsager relations are satisfied its entropy production is positive although it is minimal. We conclude discussing estimates of entropy production for partially accessible systems, comparing our results with the lower bound provided by the thermodynamic uncertainty relations.

Prethermal Time-Crystalline Spin Ice and Monopole Confinement in a Driven Magnet.

Studies of systems far from equilibrium open up new avenues for investigating exotic phases of matter. A driven-dissipative frustrated spin system is examined in this study, and we suggest an out-of-equilibrium nonmagnetic phase where the spins do not order but adhere to the ice rule in space and establish a long-range crystalline order in time. In contrast to the conventional spin ice, the dynamics of monopoles is confined due to the nonequilibrium feature of our model. Possible experimental realizations of our model are discussed.

Schizophrenia MEG Network Analysis Based on Kernel Granger Causality.

Network analysis is an important approach to explore complex brain structures under different pathological and physiological conditions. In this paper, we employ the multivariate inhomogeneous polynomial kernel Granger causality (MKGC) to construct directed weighted networks to characterize schizophrenia magnetoencephalography (MEG). We first generate data based on coupled autoregressive processes to test the effectiveness of MKGC in comparison with the bivariate linear Granger causality and bivariate inhomogeneous polynomial kernel Granger causality. The test results suggest that MKGC outperforms the other two methods. Based on these results, we apply MKGC to construct effective connectivity networks of MEG for patients with schizophrenia (SCZs). We measure three network features, i.e., strength, nonequilibrium, and complexity, to characterize schizophrenia MEG. Our results suggest that MEG of the healthy controls (HCs) has a denser effective connectivity network than that of SCZs. The most significant difference in the in-connectivity strength is observed in the right frontal network (p=0.001). The strongest out-connectivity strength for all subjects occurs in the temporal area, with the most significant between-group difference in the left occipital area (p=0.0018). The total connectivity strength of the frontal, temporal, and occipital areas of HCs exhibits higher values compared with SCZs. The nonequilibrium feature over the whole brain of SCZs is significantly higher than that of the HCs (p=0.012); however, the results of Shannon entropy suggest that healthy MEG networks have higher complexity than schizophrenia networks. Overall, MKGC provides a reliable approach to construct MEG brain networks and characterize the network characteristics.

Integrated system model of spray flash vacuum distillation with internal heat recovery

This study proposed an integrated system model for an original spray flash vacuum distillation system that enhances and leverages the thermal non-equilibrium of the flash process via active vapor extraction to realize an internal heat recovery feature, in which partial heat from hotter vapor is recovered to cooler spray residue within the same stage of feed circulation. This system contains four interlinked sub-systems: (1) an evaporation chamber in which a vacuum-promoted spray flash vaporization occurs, with an active vapor extraction and an outflow of evaporation-cooled brine, (2) a recirculation loop of feed-brine mixture, with the circulation pump, feed heater, and spray nozzle, (3) a hybrid dual-condenser combination, with the internal heat recovery from condensing vapor to the recirculating feed and a secondary cooling by an external coolant, and (4) a vacuum source that maintains vacuum conditions to the entire system as well as discharges the non-condensable gases. The pressure of vapor phase, as the major interlinked operation parameter, is in order of sequential decrease from the evaporation chamber, through condensers, to the vacuum source while the depressurization level in each sub-system is strongly coupled with other transport characteristics such as flash vapor generation in the evaporation chamber or condensing vapor flow in condensers. Thus, the integrated system model is composed of four sub-models to describe the key processes in such four sub-systems. For the modeling validation, a lab-scale experimental system is developed to provide relevant measurements. Comparisons between model predictions against measurements show a good match. Major process characteristics (such as spray flash rate, yield rate, and operating temperatures and pressures) and operational thermodynamic characteristics (such as thermal consumption and heat recovery efficiency) are investigated parametrically. The system's multivariate impacts concerning distillate yield rate and heat recovery effectiveness are also studied with varied operating parameters. Results indicate the pronounced thermal non-equilibrium feature arising from the spray flash process can be effectively utilized via the internal heat recovery design of our system to recover up to more than half of the heat from the yield vapor. Meanwhile, the developed system model can effectively analyze various operational and parametric effects, proving valuable for system design and optimized operation.

How plane are plane shock waves in solids

The notion of plane shock waves is a macroscopic, very fruitful idealization of near discontinuous disturbance propagating at supersonic speed. Such a picture is comparable to the picture of shorelines seen from a very high altitude. When viewed at the grain scale where the structure of solids is inherently heterogeneous and stochastic, features of shock waves are non-laminar and field variables, such as particle velocity and pressure, fluctuate. This paper reviews select aspects of such fluctuating nonequilibrium features of plane shock waves in solids with focus on grain scale phenomena and raises the need for a paradigm change to achieve a deeper understanding of plane shock waves in solids.

Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics.

Nonequilibrium and instability features of prey-predator-like systems associated to topological quantum domains emerging from a quantum phase-space description are investigated in the framework of the Weyl-Wigner quantum mechanics. Reporting about the generalized Wigner flow for one-dimensional Hamiltonian systems, H(x,k), constrained by ∂^{2}H/∂x∂k=0, the prey-predator dynamics driven by Lotka-Volterra (LV) equationsis mapped onto the Heisenberg-Weyl noncommutative algebra, [x,k]=i, where the canonical variables x and k are related to the two-dimensional LV parameters, y=e^{-x} and z=e^{-k}. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters for the prey-predator-like dynamics are then shown to be affected by quantum distortions over the classical background, in correspondence with nonstationarity and non-Liouvillianity properties quantified in terms of Wigner currents and Gaussian ensemble parameters. As an extension, considering the hypothesis of discretizing the time parameter, nonhyperbolic bifurcation regimes are identified and quantified in terms of z-y anisotropy and Gaussian parameters. The bifurcation diagrams exhibit, for quantum regimes, chaotic patterns highly dependent on Gaussian localization. Besides exemplifying a broad range of applications of the generalized Wigner information flow framework, our results extend, from the continuous (hyperbolic regime) to discrete (chaotic regime) domains, the procedure for quantifying the influence of quantum fluctuations over equilibrium and stability scenarios of LV driven systems.

Kinetic Nonequilibrium Signatures in the Distribution Function of Earth-Escaping Hydrogen Atoms

The lightest atmospheric gas constituents, like H- and He- atoms, are known to escape from planetary gravitational fields to open space. Hereby it counts that not only the uppermost atmospheric layer, the so-called exobase, contributes to this planetary gas escape, but the layers below do contribute as well, especially since from below a nonthermal character of the final particle outflow is induced.We consider the outflow of H - atoms from lower levels of a planetary oxygen-dominated upper atmosphere, stratified by the planet‘s gravitational field - as given in case of the Earth. The terrestrial H-atom outflow is locally modified by elastic collisions of upwards flying H-atoms with the heavy major atmospheric background constituent. This causes a collision–induced velocity-modulation of the upwards directed H-atom flow and induces nonthermal kinetic signatures of the local H ˗ atom distribution function. An important, hitherto unrespected point hereby is that angle-integrated elastic O ˗ H- collision cross sections are velocity-dependent, falling off with increasing velocity v like (1/v). Consequently this modulation influences low velocity H-atoms stronger than high-velocity ones, which changes the kinetic profile of the escaping H-atoms and causes deviations from the classic Jeans escape. Deeply down in the lower thermosphere the local H-atoms, like as well the O-atoms, indeed are in a thermodynamical equilibrium characterized by Maxwell distributions with a common temperature TH = TO. Nevertheless, at the upper exobase border of the atmosphere the resulting H-atom escape flow turns out to be a, non-equilibrium flow with non-thermal escape-relevant properties. Here we describe this collisional modification of the H-escape flow and quantify the upcome of kinetic non-equilibrium features like power laws in the wings of the H-distribution function. This collisional modulation via velocity-dependent collision cross-sections acts as a typical process to convert equilibrium distributions into non-equilibrium kappa-like distribution functions. On the basis of this theoretical approach and stabilizing the upper atmosphere by the type of so-called "iso-baric Kappa functions" which all represent the same H ˗ atom- pressure we can calculate the effective escape flux of H- atoms to open space and can quantify its difference with respect to the classical Jeans escape value. While finding again that the classical Jeans formula slightly overestimates the actual escape flux, we now for the first time taking into account the nonthermal influence of collisional modulations can show that the actual escape with respect to the actual Jeans value is even enhanced by factors 2 to 3.

Dynamic magnetic properties and phase diagrams of Fe4N system

The dynamic magnetic properties of the nonequilibrium Fe4N system are calculated on the basis of correlated effective-field theory (EFT). The dynamic phase diagrams are plotted for different values of the oscillating magnetic field and the crystal field. The reentrant behavior, the dynamic tricritical point and the dynamic critical end point observed in certain case by using EFT are established to emerge as the generic nonequilibrium features of the Fe4N system. Moreover, we compare our results with those produced by mean-field theory (MFT), and find that the first-order phase transition and the reentrant phenomena are significantly reduced due to the consideration of spin–spin thermal fluctuations in EFT approximations. Our findings lead us to conclude that the thermal fluctuations considered in EFT are a critical factor for the dynamic magnetic properties of the nonequilibrium Fe4N system.

Comparative analysis of time irreversibility and amplitude irreversibility based on joint permutation

Although time irreversibility (TIR) and amplitude irreversibility (AIR) are relevant concepts for nonequilibrium analysis, their association has received little attention. This paper conducts a systematic comparative analysis of the relationship between TIR and AIR based on statistical descriptions and numerical simulations. To simplify the quantification of TIR and AIR, the amplitude permutation and global information of the associated vector are combined to produce a joint probability estimation. Chaotic logistic, Henon, and Lorenz series are generated to evaluate TIR and AIR according to surrogate theory, and the distributions of joint permutations for these model series are measured to compare the degree of TIR and AIR. The joint permutation TIR and AIR are then used to investigate nonequilibrium pathological features in epileptic electroencephalography data. Test results suggest that epileptic brain electrical activities, particular those during the onset of seizure, manifest higher nonequilibrium characteristics. According to the statistical definitions and targeted pairs of joint permutations in the chaotic model data, TIR and AIR are fundamentally different nonequilibrium descriptors from time- and amplitude-reversibility, respectively, and thus require different forms of numerical analysis. At the same time, TIR and AIR both provide measures for fluctuation theorems associated with nonequilibrium processes, and have similar probabilistic differences in the pairs of joint permutations and consistent outcomes when used to analyze both the model series and real-world signals. Overall, comparative analysis of TIR and AIR contributes to our understanding of nonequilibrium features and broadens the scope of quantitative nonequilibrium measures. Additionally, the construction of joint permutations contributes to the development of symbolic time series analysis.