Non-equilibrium Conditions Research Articles

An optimization-based equilibrium measure describes fixed points of non-equilibrium dynamics: application to edge of chaos

Abstract Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient of a potential. These features make analytic studies very challenging. The common tool is the path integral approach or dynamical mean-field theory, but the drawback is that one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed form solutions in general. From the aspect of associated Fokker-Planck equation, the steady state solution is generally unknown. Here, we treat searching for the steady states as an optimization problem, and construct an approximate potential related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running an approximate stochastic gradient dynamics or Langevin dynamics. Only in the zero temperature limit, the distribution of the original steady states can be achieved. The resultant stationary state of the dynamics follows exactly the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method, which leads naturally to order parameters for the non-equilibrium steady states. Our theory reproduces the well-known result of edge-of-chaos, and further the order parameters characterizing the continuous transition are derived, and the order parameters are explained as fluctuations and responses of the steady states. Our method thus opens the door to analytically study the steady state landscape of the deterministic or stochastic high dimensional dynamics.

A Robust Static Model of Basic Oxygen Furnace for Analyzing Emerging Steelmaking Scenarios

A robust static model, which incorporates emerging steelmaking scenarios in terms of solid charge mix with the given hot metal in basic oxygen furnace process, is developed. It employs mass and enthalpy balances to comprehend nonequilibrium conditions, considering four key empirical parameters: iron loss, post‐combustion ratio, heat loss, and undissolved lime content in slag, which are fine‐tuned using plant data through a multivariate approach, ensuring the reliability. The model is validated in a basic oxygen furnace (BOF) shop using data from over 4000 heats, achieving a strike rate of ≈77% for input lime prediction within ±1 ton and ≈80% for input oxygen prediction within ±600 Nm3. Model implementation in BOF shop provides valuable guidance to the operators, resulting in the reduction of average oxygen and lime consumption by 139 Nm3 and 652 kg heat−1, respectively. The model also enables the determination of the maximum scrap utilization of ≈16% for 0.8% silicon and ≈14% for 0.6% silicon in hot metal, respectively. The model aids in calculating the maximum tap temperature for varying hot metal silicon and iron ore addition. Overall, the model optimizes primary steelmaking, enhancing efficiency, reducing resource consumption, and offering insights into alternative iron sources like direct reduced iron.

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.

Surface Coloring and Plasmonic Information Encryption at 50000 dpi Enabled by Direct Femtosecond Laser Printing.

Femtosecond (fs) laser pulses drive matter into a highly nonequilibrium state, allowing precise sculpturing of irradiated surface sites with sophisticated nanomorphologies. Here, we used fs-laser patterning to create diverse plasmonic morphologies on the top Au layer of the metal-insulator-metal sandwich. Mutual action of laser-driven thermomechanical effects and ultrafast solid-to-liquid transition allows control of the morphology resulting in pronounced surface reflectivity modulation, i.e., in a structural color effect. This enables template-free high-resolution color printing at a superior lateral resolution up to 50000 dots per inch and facile tunability of the color tone and saturation. Moreover, precise control over the orientation of the printed nanostructures within subwavelength lattices allows modulation of their local plasmonic response encrypting the optical information within the colorful images. The hidden information can be unveiled using a facile cross-polarized optical visualization scheme, rendering the proposed method with extra modalities combining high resolution information encryption, coloring, and security labeling.

Optical diagnostics of vacuum arcs in the process of DC interruption

Abstract Vacuum circuit-breakers (VCBs) are commonly used in emerging mechanical DC circuit-breakers. The electrical performance of VCBs in DC interruption duties has been extensively investigated, but basic physics such as the excitation temperature of plasma species, electron/vapor densities and emission of droplets in such applications were rarely reported. In this paper, we focus on how the short high frequency (HF) current pulse affects erosion of electrodes as well as generation of flying droplets by using laser shadow photography. Spectroscopy was adopted to obtain spectra and calculate the excitation temperature of CuI. Shack–Hartmann wavefront sensors were applied to measure neutral and electron density, in tests where di/dt, breaking current and the direction of the injected HF current varied. Indeed, the in-phase injection of the HF current caused an intense arc, but the pulse was too short to make either the cathode or anode melt. Since the plasma is in a nonequilibrium state, the excitation temperature of CuI is relatively low. Electron densities in different tests all approach similar values right before current zero. Neutral densities show strong fluctuation and independence on instantaneous current.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers -as caused by the additional burden of artificial genetic circuits- shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state (NESS) model of gene expression, capturing characteristics like energy dissipation -which we link to the entropy production rate- and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energy efficiency of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

Bound-state confinement after trap-expansion dynamics in integrable systems

Abstract Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin- 1 / 2 anisotropic Heisenberg chain (XXZ chain). Specifically, we consider the sudden vacuum expansion of a finite region A prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of A. Since region A is finite, at asymptotically long times bound states are ‘liberated’ after the ‘evaporation’ of the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the p-Néel states, which are obtained by repetition of a unit cell with p up spins followed by p down spins. Upon increasing p, the bound-state content is enhanced. In the limit p → ∞ one obtains the domain-wall initial state. We show that for p < 4, only bound states with n > p are confined at large chain anisotropy. For p ≳ 4 , bound states with n = p are also confined, consistent with the absence of transport in the limit p → ∞ . The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.

Nonequilibrium Membrane Dynamics Induced by Active Protein Interactions and Chemical Reactions: A Review

AbstractBiomembranes wrapping cells and organelles are not only the partitions that separate the insides but also dynamic fields for biological functions accompanied by membrane shape changes. In this review, we discuss the spatiotemporal patterns and fluctuations of membranes under nonequilibrium conditions. In particular, we focus on theoretical analyses and simulations. Protein active forces enhance or suppress the membrane fluctuations; the membrane height spectra are deviated from the thermal spectra. Protein binding or unbinding to the membrane is activated or inhibited by other proteins and chemical reactions, such as ATP hydrolysis. Such active binding processes can induce traveling waves, Turing patterns, and membrane morphological changes. They can be represented by the continuum reaction‐diffusion equations and discrete lattice/particle models with state flips. The effects of structural changes in amphiphilic molecules on the molecular‐assembly structures are also discussed.

Analytical solutions for the advective–diffusive ice column in the presence of strain heating

Abstract. A thorough understanding of ice thermodynamics is essential for an accurate description of glaciers, ice sheets and ice shelves. Yet there exists a significant gap in our theoretical knowledge of the time-dependent behaviour of ice temperatures due to the inevitable compromise between mathematical tractability and the accurate description of physical phenomena. In order to bridge this shortfall, we have analytically solved the 1D time-dependent advective–diffusive heat problem including additional terms due to strain heating and depth-integrated horizontal advection. Newton's law of cooling is applied as a Robin-type top boundary condition to consider potential non-equilibrium temperature states across the ice–air interface. The solution is expressed in terms of confluent hypergeometric functions following a separation of variables approach. Non-dimensionalization reduces the parameter space to four numbers that fully determine the shape of the solution at equilibrium: surface insulation, effective geothermal heat flow, the Péclet number and the Brinkman number. The initial temperature distribution exponentially converges to the stationary solution. Transient decay timescales are only dependent on the Péclet number and the surface insulation, so higher advection rates and lower insulating values imply shorter equilibration timescales, respectively. In contrast, equilibrium temperature profiles are mostly independent of the surface insulation parameter. We have extended our study to a broader range of vertical velocities by using a general power-law dependence on depth, unlike prior studies limited to linear and quadratic velocity profiles. Lastly, we present a suite of benchmark experiments to test numerical solvers. Four experiments of gradually increasing complexity capture the main physical processes for heat propagation. Analytical solutions are then compared to their numerical counterparts upon discretization over unevenly spaced coordinate systems. We find that a symmetric scheme for the advective term and a three-point asymmetric scheme for the basal boundary condition best match our analytical solutions. A further convergence study shows that n≥15 vertical points are sufficient to accurately reproduce the temperature profile. The solutions presented herein are general and fully applicable to any problem with an equivalent set of boundary conditions and any given initial temperature distribution.

Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems

We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to N=100 spins.

Grain boundary diffusion in additively manufactured CoCrFeMnNi high-entropy alloys: Impact of non-equilibrium state, temperature and relaxation

Grain boundary diffusion of Ni in the equiatomic CoCrFeMnNi high-entropy alloy, produced by additive manufacturing, is measured using a radiotracer technique in an extended temperature interval of 350 to 703 K. A strongly non-monotonic temperature dependence of the Ni grain boundary diffusion coefficients (with a spectacular intermittent retardation of the diffusion rates with increasing temperature) is seen and explained by relaxation of a non-equilibrium state induced by rapid solidification during fabrication. The grain boundary excess energy of the non-equilibrium state of these grain boundaries, as estimated from the diffusion data, is found to be larger than 0.3 J/m2. This corresponds to an increase of about 30% of the interface energy compared to relaxed general high-angle grain boundaries. The temperature-induced evolution of the grain boundary state is analyzed in terms of the concomitant structure evolution, segregation, phase stability and precipitation in the multi-component alloy.

Role of nanostructured surface layers in enhancing pure titanium diffusion bonding above their destabilization temperatures

The benefits of the nanostructured materials are believed to be probably absent if they are used at high temperatures. In this study, enhanced diffusion bonding of pure Ti was investigated by introducing a nanostructured surface layer through the surface mechanical attrition treatment (SMAT) technique. Complete recrystallization and remarkable grain growth have taken place in the original nanostructured surface layer due to the diffusion bonding conditions far beyond the nanostructured Ti destabilization temperatures. However, they still played a significant role in enhancing the Ti/Ti interfacial bonding. The consistency analysis of relative grain boundary energy, relaxation time, and microstrain reveals that although the original nanocrystalline has disappeared, the newly formed grain boundaries (GBs) during recrystallization probably inherit part of non-equilibrium state of the corresponding GBs in the as-SMATed surface layer, where the atomic diffusivity may increase greatly compared to the general relaxed GBs in their coarse-grained polycrystalline counterparts. The presence of these high-energy non-equilibrium GBs retains ultrafast atomic diffusion paths, leading to a diffusion bonding temperature of at least 100 °C lower than the traditional approach. The joint achieved at a low temperature of 750 °C exhibited a shear strength approximately 2 times higher than that prepared using raw substrates.

Free-energy transduction mechanisms shape the flux space of metabolic networks

The transduction of free energy in metabolic networks represents a thermodynamic mechanism by which the free energy derived from nutrients is converted to drive nonspontaneous, energy-requiring metabolic reactions. This transduction is typically observed in processes that generate energy-rich molecules such as ATP and NAD(P)H, which, in turn, power specific reactions, particularly biosynthetic reactions. This property establishes a pivotal connection between the intricate topology of metabolic networks and their ability to redirect energy for functional purposes. The present study proposes a dedicated framework aimed at exploring the relationship between free-energy dissipation, network topology, and metabolic objectives. The starting point is that, regardless of the network topology, nonequilibrium chemostatting conditions impose stringent thermodynamic constraints on the feasible flux steady states to satisfy energy and entropy balances. An analysis of randomly sampled reaction networks shows that the network topology imposes additional constraints that restrict the accessible flux solution space, depending on key structural features such as the reaction’s molecularity, reaction cycles, and conservation laws. Notably, topologies featuring multimolecular reactions that implement free-energy transduction mechanisms tend to extend the accessible flux domains, facilitating the achievement of metabolic objectives such as anabolic flux maximization or flux rerouting capacity. This approach is applied to a coarse-grained model of carbohydrate metabolism, highlighting the structural requirements for optimal biomass yield.

Convective heat transfer in porous channel with multi-layer fractures under Local thermal non-equilibrium condition

Based on Brinkman-extended-Darcy model and Local thermal non-equilibrium (LTNE) model, analytical solutions of velocity and temperature fields, pressure drop and Nusselt number of porous channels containing different number of fracture layers are obtained. The characteristics of fluid flow and heat transfer in multi-layer parallel fractured channels are further studied. Results show that for a single-layer or multi-layer fractured channel, the pressure drop changes sensitively at small hollow ratio and increases as the number of fracture layers increases with decreasing increase degree, but the pressure drop tends to be consistent regardless of the number of fracture layers when Darcy number is high. For small ratio of effective thermal conductivity, LTE model is valid regardless of Biot number, and the heat transfer intensity in multi-layer fractured channels is always higher than that in single-layer fractured channel at any hollow ratio, but the heat transfer intensity is still low. For large ratio of effective thermal conductivity, increasing Biot number or fracture layer number makes the Nusselt number increase under very small hollow ratio for both single and multiple fracture cases, and when both the ratio of effective thermal conductivity and Biot number are high, there is an intersection point occurs at hollow ratio near 0.1, which makes same heat transfer effect under different fracture numbers.

Dynamic Partitioning of Surfactants into Nonequilibrium Emulsion Droplets.

Characterizing the propensity of molecules to distribute between fluid phases is key to describing chemical concentrations in heterogeneous mixtures and the corresponding physiochemical properties of a system. Typically, partitioning is studied under equilibrium conditions. However, some mixtures form a single phase at equilibrium but exist in multiple phases when out-of-equilibrium, such as oil-in-water emulsion droplets stabilized by surfactants. Such droplets persist for extended times but ultimately disappear due to droplet dissolution and micellar solubilization. Consequently, equilibrium properties like oil-water partition coefficients may not accurately describe out-of-equilibrium droplets. This study investigates the partitioning of nonionic surfactants between shrinking microscale oil droplets and water under nonequilibrium conditions. Quantitative mass spectrometry is used to analyze the composition of individual microdroplets over time under conditions of varying surfactant composition, concentrations, and oil molecular structures. Within minutes, nonionic surfactants partition into oil droplets, reaching a nonequilibrium steady-state concentration that can be over an order of magnitude higher than that in the aqueous phase. As the droplets solubilize over hours, the surfactants are released back into water, leading to transiently high surfactant concentrations near the droplet-water interface and the formation of a microemulsion phase with a low interfacial tension. Introducing ionic surfactants that form mixed micelles with nonionic surfactants reduces partitioning. Based on this observation, stimuli-responsive ionic surfactants are used to modulate the nonionic surfactant partitioning and trigger reversible phase separation and mixing inside binary oil droplets. This study reveals generalizable nonequilibrium states and conditions experienced by solubilizing oil droplets that influence emulsion properties.

Semi-infinite Simple Exclusion Process: From Current Fluctuations to Target Survival.

The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but so far most results are restricted to two geometries: (i)a finite system between two reservoirs, which does not conserve the number of particles but reaches a nonequilibrium steady state, and (ii)an infinite system which conserves the number of particles but never reaches a steady state. Here, we obtain an expression for the full cumulant generating function of the integrated current in the important intermediate situation of a semi-infinite system connected to a reservoir, which does not conserve the number of particles and never reaches a steady state. This results from the determination of the full spatial structure of the correlations, which we infer to obey the very same closed equation recently obtained in the infinite geometry and argue to be exact. Besides their intrinsic interest, these results allow us to solve two open problems: the survival probability of a fixed target in the SEP, and the statistics of the number of particles injected by a localized source.

Influence of Solid-Phase and Melt-Quenching Na3Fe2(PO4)3 Polycrystal Production Technology on Their Structure and Ionic Conductivity

This article studies the influence of solid-phase (type 1 samples) and melt-quenching (type 2 samples) technological modes of obtaining Na3Fe2(PO4)3 polycrystals on their structures and ion-conducting properties. α-Na3Fe2(PO4)3 polycrystals of the 1st type are formed predominantly under an isothermal firing regime, and the synthesis of the 2nd type is carried out under sharp temperature gradient conditions, contributing to the formation of glassy precursors possessing a reactive and deformed structure, in which the crystallization of crystallites occurs faster than in precursors obtained under isothermal firing. The elemental composition of α-Na3Fe2(PO4)3 type 2 polycrystals is maintained within the normal range despite the sharp non-equilibrium thermodynamic conditions of synthesis. The microstructure of the type 1 Na3Fe2(PO4)3 polycrystals is dominated by chaotically arranged crystallites of medium (7–10 μm) and large (15–35 μm) sizes, while the polycrystals of type 2 are characterized by the preferential formation of small (3–4 μm) and medium (7–10 μm) crystallites, causing uniaxial deformations in their structure, which contribute to a partial increase in their symmetry. The advantage of type 2 polycrystals is that they have higher density and conductivity and are synthesized faster than type 1 samples by a factor of 4. The article also considers the issues of crystallization in a solid-phase precursor from the classical point of view, i.e., the process of the formation of small solid-phase nuclei in the metastable phase and their growth to large particles due to association with small crystallites using phase transitions. Possible variants and models of crystallite growth in Na3Fe2(PO4)3 polycrystals, as well as distinctive features of crystallization between two types of samples, are discussed.

Membrane Adsorption Enhances Translocation of Antimicrobial Peptide Buforin 2.

Despite ongoing research on antimicrobial peptides (AMPs) and cell-penetrating peptides (CPPs), their precise translocation mechanism remains elusive. This includes Buforin 2 (BF2), a well-known AMP, for which spontaneous translocation across the membrane has been proposed but a high barrier has been calculated. Here, we used computer simulations to investigate the effect of a nonequilibrium situation where the peptides are adsorbed on one side of the lipid bilayer, mimicking experimental conditions. We demonstrated that the asymmetric membrane adsorption of BF2 enhances its translocation across the lipid bilayer by lowering the energy barrier by tens of kJ mol-1. We showed that asymmetric membrane adsorption also reduced the free energy barrier of lipid flip-flop but remained unlikely even at BF2 surface saturation. These results provide insight into the driving forces behind membrane translocation of cell-penetrating peptides in nonequilibrium conditions, mimicking experiments.

Machine learning assisted sorting of active microswimmers.

Active matter systems, being in a non-equilibrium state, exhibit complex behaviors, such as self-organization, giving rise to emergent phenomena. There are many examples of active particles with biological origins, including bacteria and spermatozoa, or with artificial origins, such as self-propelled swimmers and Janus particles. The ability to manipulate active particles is vital for their effective application, e.g., separating motile spermatozoa from nonmotile and dead ones, to increase fertilization chance. In this study, we proposed a mechanism-an apparatus-to sort and demix active particles based on their motility values (Péclet number). Initially, using Brownian simulations, we demonstrated the feasibility of sorting self-propelled particles. Following this, we employed machine learning methods, supplemented with data from comprehensive simulations that we conducted for this study, to model the complex behavior of active particles. This enabled us to sort them based on their Péclet number. Finally, we evaluated the performance of the developed models and showed their effectiveness in demixing and sorting the active particles. Our findings can find applications in various fields, including physics, biology, and biomedical science, where the sorting and manipulation of active particles play a pivotal role.

Metastable phases of Ag–Si: amorphous Si and Ag-nodule mediated bonding

Metastable phases such as supersaturated solid solutions, supercooling, and amorphous phases are well-known in metallurgy. They are often composed in non-equilibrium states and can be transformed into a stable phase by overcoming an energy barrier with driving forces. Particularly, it has been widely used for material strengthening and heterogeneous nucleation of precipitates in solids is mainly induced by heat treatments for supersaturated solid solutions. However, little is known about the metastable phases of the Ag–Si alloy, although it is a well-known simple binary eutectic alloy. Here, we show that the metastable phases composed of amorphous Si and supersaturated Ag solid solution are induced by the eutectic reaction under rapid cooling of Ag–Si. Furthermore, the solute Si in the Ag matrix reacts with oxygen to precipitate Ag by-products, which grow as nodules. The Ag nodules have high crystallinity and robust interfacial structures, and the nodule growth leads to the formation of cross-links between the Ag–Si particles. We also demonstrate the Ag nodule-mediated bonding where the rapidly cooled Ag–Si ribbon is directly used as a bonding medium, indicating the possibility of using it as a high-temperature bonding material with low-temperature processes.