Non-equilibrium Conditions Research Articles

Thermodynamic circuits: Association of devices in stationary nonequilibrium.

For a circuit made of thermodynamic devices in stationary nonequilibrium, we determine the mean currents (of energy, matter, charge, etc.) exchanged with external reservoirs driving the circuit out of equilibrium. Starting from the conductance matrix describing the nonlinear current-force characteristics of each device, we obtain the conductance matrix of the composite device. This generalizes the rule of resistance addition (serial association) or conductance addition (parallel association) in stationary out-of-equilibrium thermodynamics and for multiple coupled potentials and currents of different natures. Our work emphasizes the pivotal role of conservation laws when creating circuits of complex devices. Finally, two examples illustrate among others the determination of the conservation laws for the serial and parallel associations of thermodynamic devices.

Photoswitchable Imines Drive Dynamic Covalent Systems to Nonequilibrium Steady States.

Coupling a photochemical reaction to a thermal exchange process can drive the latter to a nonequilibrium steady state (NESS) under photoirradiation. Typically, systems use separate motifs for photoresponse and equilibrium-related processes. Here, we show that photoswitchable imines can fulfill both roles simultaneously, autonomously driving a dynamic covalent system into a NESS under continuous light irradiation. We demonstrate this using transimination reactions, where E-to-Z photoisomerism generates a more kinetically labile species. At the NESS, energy is stored both in the metastable Z-isomer of the imine and in the system's nonequilibrium constitution; when the light is switched off, this stored energy is released as the system reverts to its equilibrium state. The system operates autonomously under continuous light irradiation and exhibits characteristics of a light-driven information ratchet. This is enabled by the dual-role of the imine linkage as both the photochromic and dynamic covalent bond. This work highlights the ability and application of these imines to drive systems to NESSs, thus offering a novel approach in the field of systems chemistry.

CLT for NESS of a reaction-diffusion model

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions d≤3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d \\le 3$$\\end{document} we show a central limit theorem for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.

Unlocking the unfolded structure of ubiquitin: Combining time-resolved x-ray solution scattering and molecular dynamics to generate unfolded ensembles.

The unfolding dynamics of ubiquitin were studied using a combination of x-ray solution scattering (XSS) and molecular dynamics (MD) simulations. The kinetic analysis of the XSS ubiquitin signals showed that the protein unfolds through a two-state process, independent of the presence of destabilizing salts. In order to characterize the ensemble of unfolded states in atomic detail, the experimental XSS results were used as a constraint in the MD simulations through the incorporation of x-ray scattering derived potential to drive the folded ubiquitin structure toward sampling unfolded states consistent with the XSS signals. We detail how biased MD simulations provide insight into unfolded states that are otherwise difficult to resolve and underscore how experimental XSS data can be combined with MD to efficiently sample structures away from the native state. Our results indicate that ubiquitin samples unfolded in states with a high degree of loss in secondary structure yet without a collapse to a molten globule or fully solvated extended chain. Finally, we propose how using biased-MD can significantly decrease the computational time and resources required to sample experimentally relevant nonequilibrium states.

Influence of multiphase microstructure on the strength and ductility of Nb–Zr–Ti–V refractory high entropy alloys

In this investigation, we focused on the lightweight Nb–Zr–Ti–V alloys as representative model alloys to explore improving mechanical properties of refractory high entropy alloys (RHEAs) through phase engineering. The alloys were deliberately designed with different element concentrations and varied cooling rates after homogenization treatment, resulting in formation of multiple secondary phases. Microstructures of prepared alloys were reported, revealing the decomposition of the BCC matrix into dual-BCC phases with increasing V content. We attribute this phenomenon to the substantial atomic size misfit between V and Zr. Additionally, a metastable FCC phase and an intermetallic Laves phase emerged at intermediate temperatures in Nb0.75ZrTiV0.75, influenced by the nonequilibrium condition during cooling and the enthalpic effect. Compression tests were performed to access mechanical characteristics of different phases. The dual-BCC phases, featuring granular or multilayer morphology, enhanced ductility of the alloy by facilitating dislocation movement at BCC interfaces. In contrast, the FCC and Laves phases, characterized by a needle-like morphology, increased strength of the alloy owing to their intrinsic hardness. Based on the current discovery and understanding on secondary phases in the Nb–Zr–Ti–V alloys, our future objective is to obtain a modulated microstructure with an appropriate combination of different phases to optimize strength and ductility simultaneously.

A device for dynamic testing of the refractory ceramic resistance to biomass ash

The corrosive effects of biomass ash on refractory materials in combustion chambers pose challenges. Development of new castable refractory materials which are more resistant to corrosion requires tests that accurately reflect the conditions occurring in real devices. This article describes the Computational Fluid Dynamics (CFD) design and construction of a device for evaluating the corrosion of refractory materials in dynamic regime. The device allows to simulate combustion chamber conditions accurately, to regulate an injection of corrosive medium on the tested material surface under the specified conditions (temperature, time, and flow). In the present investigation the conventional refractory material was exposed to attack of biomass ash at the temperature of 1300 °C for 3 h to test the functionality of the device. A burner with technology oxygen–enriched combustion was used to heat the device. The corrosion tests were conducted in accordance with the standard P CEN/TS 15,418 and the standard STN EN ISO 21404. The operational state required for corrosion tests at 1300 °C was achieved within 1.12 h. The extent of refractory material degradation in the dynamic corrosion regime was evaluated using electron microscopy-energy dispersive spectroscopy (EM-EDS) and compared with the results of a static crucible test (3 h at 1300 °C). The dynamic test provided sufficient information on the interactions of corrosion medium with the refractories. Its main advantages are the maintenance of non-equilibrium conditions by controlled deposition of the corrosion medium in quantity from 1 to −100 g/h, fast heating rate to operating temperature (20 °C/min), and the possibility of conditions variability during tests (temperature, ox-red. atmosphere, fuel gas flow etc.).

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

Kinetically Controlled and Nonequilibrium Assembly of Block Copolymers in Solution.

Covalent polymers are versatile macromolecules that have found widespread use in society. Contemporary methods of polymerization have made it possible to construct sequence polymers, including block copolymers, with high precision. Such copolymers assemble in solution when the blocks have differing solubilities. This produces nano- and microparticles of various shapes and sizes. While it is straightforward to draw an analogy between such amphiphilic block copolymers and phospholipids, these two classes of molecules show quite different assembly characteristics. In particular, block copolymers often assemble under kinetic control, thus producing nonequilibrium structures. This leads to a rich variety of behaviors being observed in block copolymer assembly, such as pathway dependence (e.g., thermal history), nonergodicity and responsiveness. The dynamics of polymer assemblies can be readily controlled using changes in environmental conditions and/or integrating functional groups situated on polymers with external chemical reactions. This perspective highlights that kinetic control is both pervasive and a useful attribute in the mechanics of block copolymer assembly. Recent examples are highlighted in order to show that toggling between static and dynamic behavior can be used to generate, manipulate and dismantle nonequilibrium states. New methods to control the kinetics of block copolymer assembly will provide endless unanticipated applications in materials science, biomimicry and medicine.

Duality for the multispecies stirring process with open boundaries

We study the stirring process with N − 1 species on a generic graph G=(V,E) with reservoirs. The multispecies stirring process generalizes the symmetric exclusion process, which is recovered in the case N = 2. We prove the existence of a dual process defined on an extended graph G~=(V~,E~) which includes additional sites in V~∖V where dual particles get absorbed in the long-time limit. We thus obtain a characterization of the non-equilibrium steady state of the boundary-driven system in terms of the absorption probabilities of dual particles. The process is integrable for the case of the one-dimensional chain with two reservoirs at the boundaries and with maximally one particle per site. We compute the absorption probabilities by relying on the underlying gl(N) symmetry and the matrix product ansatz. Thus one gets a closed-formula for (long-ranged) correlations and for the non-equilibrium stationary measure. Extensions beyond this integrable set-up are also discussed.

Signals of detailed balance violation in nonequilibrium stationary states: subtle, manifest, and extraordinary

The evolution of physical systems are often modeled by simple Markovian processes. When settled into stationary states, the probability distributions of such systems are time independent, by definition. However, they do not necessarily fall within the framework of equilibrium statistical mechanics. Instead, they may be non-equilibrium steady states (NESS). One distinguishing feature of NESS is the presence of time reversal asymmetry (TRA) and persistent probability current loops. These loops lead naturally to the notion of probability angular momenta, which play a role on the same footing as the noise covariance in stochastic processes. Illustrating with simulations of simple models and physical data, we present ways to detect these signals of TRA, from the subtle to the prominent.

Entropy Theory in the Context of Physics Education

Entropy, initially a concept in thermodynamics describing the degree of disorder in a system, has been extended to information theory and non-equilibrium thermodynamics. The article proposes that the physical classroom teaching system can be viewed as a dissipative structure, promoting the orderly development of students' cognition through openness, non-equilibrium states, and fluctuation mechanisms. Specific strategies include opening up teaching content and methods, creating non-equilibrium state experiments, introducing cognitive fluctuations, and utilizing non-linear effects. These approaches help to stimulate students' desire for knowledge, optimize the teaching process, and achieve efficient physical classroom teaching.

Austenite Growth Behavior and Prediction Modeling of Ti Microalloyed Steel.

Previous studies on the austenite grain growth were mostly based on a fixed temperature, and the relationship between the austenite grain and austenitizing parameters was fitted according to the results. However, there is a lack of quantitative research on the austenite grain growth during the heating process. In the present work, based on the diffusion principle of the controlled Ti microalloying element, the diffusion process of carbonitrides containing Ti during the heating process was analyzed. Combined with the precipitation model and the austenite growth model, the prediction model of austenite grain growth of Ti microalloyed steel during different heat treatment processes was established. The austenite grain size versus the temperature at four different heating rates of 0.5, 1, 10, 100 °C/s was calculated. The grain growth behavior of austenite during the heating process of Ti microalloyed steel was studied by optical microscope, scanning electron microscope and transmission electron microscope. The experimental data of the austenite grain size was in good agreement with the calculation by the proposed model, which provides a new idea for the prediction of austenite grain size in non-equilibrium state during the heating process. In addition, for Ti-containing microalloyed steels, the austenite grain size increased with the increasing heating temperature, while it changed little by further prolonging isothermal time after certain heating time, which was related to the equilibrium degree of the precipitation and the dissolution of Ti element. The austenite grain coarsening temperature of the tested Ti microalloyed steel was estimated within 1100~1200 °C.

New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers

AbstractA fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm.

Establishing mechanisms for nonlinear collector tribodynamics of magnetization under ferroresonance regimes

The paper considers a parallel electromagnetic oscillating circuit with a nonlinear inductance under conditions of excitation of ferroresonances. Physical mechanisms of dynamic self-regulation of the system of spin magnetic moments of ferromagnetic and ferrimagnetic dielectrics in the surrounding magnetic field are established. It is shown that upon entering the magnetic saturation regime, the effect of dynamic antiferroresonance is observed, due to the cyclic reversal of magnetization in the internal magnetic field. This effect has a collector character and corresponds to the maximum potential energy of the magnetic moment in the field and the antiparallel orientation of the moment with respect to the field. Such regimes are realized in thermodynamically non-equilibrium conditions and are correlated with unstable equilibrium positions of the corresponding mechanical analogues. The resulting forms of oscillations correlate with the dynamics of an inverted pendulum and have a significantly non-harmonic character. Autosynchronization of frequencies and nonlinear mixing of such forms with quasi-static modes imitating the time form of external excitation of oscillations were revealed. It is shown that the nonlinearity of ferromagnetic elements self-limits the height of resonance maxima. And on the other hand, it contributes to the cascade transport of energy by the spectrum of disturbances, which can have negative consequences when exciting low-frequency ferroresonances in power grids. The effect of dynamic antiferroresonance has the opposite direction to the known quasi-static behavior of the system of spin magnetic moments in an external field and must be taken into account when calculating and operating electrical systems with nonlinear inductances. Examples of collector self-oscillating modes similar in their physical mechanisms in nonlinear contact tribodynamics systems are given

Chemical composition from photos: Dried solution drops reveal a morphogenetic tree

Under nonequilibrium conditions, inorganic systems can produce a wealth of life-like shapes and patterns which, compared to well-formed crystalline materials, remain widely unexplored. A seemingly simple example is the formation of salt deposits during the evaporation of sessile droplets. These evaporites show great variations in their specific patterns including single rings, creep, small crystals, fractals, and featureless disks. We have explored the patterns of 42 different salts at otherwise constant conditions. Based on 7,500 images, we show that distinct pattern families can be identified and that some salts (e.g., Na2SO4 and NH4NO3) are bifurcated creating two distinct motifs. Family affiliations cannot be predicted a priori from composition alone but rather emerge from the complex interplay of evaporation, crystallization, thermodynamics, capillarity, and fluid flow. Nonetheless, chemical composition can be predicted from the deposit pattern with surprisingly high accuracy even if the set of reference images is small. These findings suggest possible applications including smartphone-based analyses and lightweight tools for space missions.

Thermo-chemical nonequilibrium effects on combustion characteristics of a transverse jet in the scramjet

As the Mach number increases, the local static temperature gradually approaches the characteristic gas vibration/dissociation temperature, and significant thermo-chemical relaxation processes occur. The thermo-chemical nonequilibrium phenomenona could affect the mixing and combustion process and become a factor that must be considered for scramjet design. In this paper, a large eddy simulation solver based on the two-temperature model is developed. The transfer terms between vibrational and trans-rotational energy are modeled by the Landau–Teller formulation and the vibrational-dissociation coupling is considered by adopting the Park model. Three sets of simulations based on the Hyshot Ⅱ engine configuration with different models were performed simultaneously to validate numerical methods and analyze results. The results reveal that the shock, cross-injection of fuel, and Prandtl-Meyer flow induce significant nonequilibrium regions. The vibration relaxation process in the jet mixing region is frozen, the vibration temperature is much higher than the trans-rotational temperature, and the extra energy is converted from the vibration mode to the trans-rotational mode, resulting in the increase of the trans-rotational temperature and the advance of auto-ignition in the nonequilibrium condition. Considering the vibration-dissociation coupling, the higher vibration temperature promotes dissociation. It inhibits the generation of active radicals in the ignition process, weakening the enhancement effect of nonequilibrium on auto-ignition. In the expanded nozzle, the concentrations of molecules and trans-rotational temperature in nonequilibrium cases are slightly lower than those in the equilibrium case due to the enhancement of dissociation.

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Abstract This paper presents a comprehensive framework for analyzing phase transitions in collective models like the Vicsek model under various noise types. The Vicsek model, focuses on understanding the collective behaviors of social animals, is known for its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium state, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noise. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with the escalation of population density.

The remarkable effects of the non-volatile matrix of wine on the release of volatile compounds evaluated by analysing their release to the headspaces

Six Spanish wines with different wine-making styles were completely dearomatised and later reconstituted to their original volume with a standard volatile solution containing 15 wine aroma compounds with broad differences in physicochemical characteristics. The headspace composition of the reconstituted wines was evaluated using an automated dynamic headspace (DHS) method combined with thermal desorption (TD) and gas chromatography–mass spectrometry (GC–MS). This method provides a snapshot of the volatile profiles transferred to the headspace in non-equilibrium conditions. The results showed that the non-volatile matrix of the wine significantly affected the transference to the headspace of the 15 aroma compounds. Differences between wines for butanoic and hexanoic acids, DMS and vanillin are above factors 5, 4 or 3, respectively, while for ethyl acetate, ethyl decanoate, 3-methylbutan-1-ol, 2-phenylethan-1-ol or 4-ethylphenol are close to a factor 2. Only ethyl butanoate was uniformly transferred. The release of DMS was related to copper levels, while pH explained part of the release of fatty acids. However, most effects of volatility are difficult to explain. Results strongly indicate that a sample-specific correction for volatility is required to interpret the sensory effects of aroma volatiles.

Local Self-Assembly of Dissipative Structures Sustained by Substrate Diffusion.

The coupling between energy-consuming molecular processes and the macroscopic dimension plays an important role in nature and in the development of active matter. Here, we study the temporal evolution of a macroscopic system upon the local activation of a dissipative self-assembly process. Injection of surfactant molecules in a substrate-containing hydrogel results in the local substrate-templated formation of assemblies, which are catalysts for the conversion of substrate into waste. We show that the system develops into a macroscopic (pseudo-)non-equilibrium steady state (NESS) characterized by the local presence of energy-dissipating assemblies and persistent substrate and waste concentration gradients. For elevated substrate concentrations, this state can be maintained for more than 4 days. The studies reveal an interdependence between the dissipative assemblies and the concentration gradients: catalytic activity by the assemblies results in sustained concentration gradients and, vice versa, continuous diffusion of substrate to the assemblies stabilizes their size. The possibility to activate dissipative processes with spatial control and create long lasting non-equilibrium steady states enables dissipative structures to be studied in the space-time domain, which is of relevance for understanding biological systems and for the development of active matter.

Steady-state probabilities for Markov jump processes in terms of powers of the transition rate matrix.

Several types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N - 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions.