Nonequilibrium Phase Transition Research Articles

Nonequilibrium thermodynamics and phase transition of Ehrenfest urns with interactions

Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle distributions. As the inter-particle attraction varies, a first order non-equilibrium phase transition occurs between these two NESSs characterized by a coexistence regime. The phase boundaries, the NESS particle distributions near saddle points and the associated particle fluxes, average urn population fractions, and the relaxational dynamics to the NESSs are obtained analytically and verified numerically. A generalized non-equilibrium thermodynamics law is also obtained, which explicitly identifies the heat, work, energy and entropy of the system.

The unstable thermoelectric effect in non-stoichiometric Cu2Se during the non-equilibrium phase transition

The superionic α ↔ β phase transition in Cu1.96Se thermoelectric material is investigated by means of thermal analysis (DSC) and measurements of Seebeck coefficient and electrical conductivity. Results of the DSC measurements with 1–10 K/min heating and cooling rates show that the material is close to the equilibrium phase composition during the transformation. However, the kinetic limitation of the process exists, which is indicated by supercooling. At the beginning of the β → α transition, the most significant kinetic delay was attributed to the nucleation of the α phase. During the phase transformation, the Seebeck coefficient was lower than in a stabilised material (measured with 0.1 K/min heating/cooling rate). During cooling, a decrease from 130 μV/K (in a stabilised measurement) to 7 μV/K (5 K/min cooling rate) was observed. The deviation from the expected values of the Seebeck coefficient was correlated with the difference between the actual and equilibrium phase compositions.Graphical abstract

Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation.

Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.

Growth transitions and critical behavior in the non-equilibrium aggregation of short, patchy nanorods.

We have carried out Monte Carlo simulations to study the non-equilibrium aggregation of short patchy nanorods in two dimensions. Below a critical value of patch size ([Formula: see text]), the aggregates have finite sizes with small radii of gyration, [Formula: see text]. At [Formula: see text], the average radius of gyration shows a power law increase with time such that [Formula: see text], where [Formula: see text]. Above, [Formula: see text], the aggregates are fractal in nature and their fractal dimension depends on the value of patch size. These morphological differences are due to the fact that below the critical value of patch size ([Formula: see text]), the growth of the clusters is suppressed and the system reaches an 'absorbed state.' Above [Formula: see text], the system reaches an 'active state,' in which the cluster size keeps growing with a fixed rate at long times. Thus, the system encounters a non-equilibrium phase transition. Close to the transition, the growth rate scales as [Formula: see text], where [Formula: see text]. The long-time growth rate varies as [Formula: see text] where [Formula: see text]. These scaling exponents indicate that the transition belongs to the directed percolation universality class. The patchy nanorods also display a threshold patch size ([Formula: see text]), beyond which the long-time growth rate remains constant. We present geometric arguments for the existence of [Formula: see text]. The fractal dimension of the aggregates increases from 1.75, at [Formula: see text], to 1.81, at [Formula: see text]. It remains constant beyond [Formula: see text].

Critical behavior of the Ising model under strong shear: The conserved case

The non-equilibrium phase transitions of the two-dimensional magnetization-conserved Ising model under the action of an external shear field is investigated. This field, that simulates a convective velocity profile with shear rate γ̇, introduces anisotropic effects and forces the system to evolve into non equilibrium states. By employing the short-time dynamics (STD) methodology, it was possible to detect first- and second-order phase transitions, and in this last case the critical exponent were calculated. As a function of the absolute magnetization |M| the system exhibits phase transitions of different order. On the one hand, If |M|=0, the model undergoes a second-order phase transition. The estimated critical temperature Tc depends on γ̇ and two regimes can be distinguished: a power-law regime for low γ̇′s, and a saturation regime at larger values of it. For the investigated shear field interval, the estimated values of the anisotropic critical exponents suggest that the critical behavior is on a crossover between the Ising and mean-field critical behaviors, respectively. On the other hand if |M|>0, the model exhibits for each γ̇ first-order phase transitions, ending in a critical point at |M|=0.

Dynamic entropy of human blood

Temperature control is a process that is used by biological systems to maintain a stable internal state for survival. People have an individually variable physiological temperature of about 36.6 °C, which can be modified by many undesirable factors. Based on an analysis of a time series of extracellular ionic fluxes that were obtained using the non-invasive solute-semiconductor interface technique, I show that this extremely specific (critical) temperature is encoded by a local minimum in the dynamic entropy of an isolated drop of human blood. Moreover, a dynamic zeroth-order normal fluid/“superfluid” nonequilibrium phase transition, which was reflected by a spontaneous symmetry breaking that occurred in the phase space, was revealed. The critical scaling of the dynamic measures for the covariates such as the spectral signature and Lyapunov exponent was also determined.

Deterministic model of battery, uphill currents, and nonequilibrium phase transitions.

We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounce-back mechanism acts when the number of particles flowing in one direction exceeds a given threshold T. In that case, the particles invert their horizontal velocity, as if colliding with vertical walls. The second channel is divided in two halves parallel to the first but located in the opposite sides of the cavities. In the second channel, motion is free. We show that, suitably tuning the sizes of cavities of the channels and of T, nonequilibrium phase transitions take place in the N→∞ limit. This induces a stationary current in the circuit, thus modeling a kind of battery, although our model is deterministic, conservative, and time reversal invariant.

The analysis of particles behavior under a delayed tristable system driven by multiplicative and additive noises

In this paper, the motion of Brownian particles driven by a delayed tristable system with multiplicative and additive Gaussian white noise is mainly studied. First, the effective potential function and stable state probability density function (PDF) are derived by using the theory of small-time delay approximation and the approximate Fokker–Planck equation (FPE), and the expression of mean first-passage times (MFPTs) is obtained by using the definition of the MFPTs and the steepest descent method. Then, the effects of the parameters which include noise intensities of multiplicative and additive noise, and correlation strength between two noises, and time delay, and the strength of time-delayed feedback on PDF and MFPTs are analyzed. Results demonstrate that the additive noise intensity has a more profound influence on PDF than the multiplicative noise intensity. The non-equilibrium phase transition of the system can be produced by the correlation strength of noises. In addition, in the behavior of the MFPTs, we can observe the noise-enhanced stability (NES) phenomenon induced by multiplicative noise intensity. Besides, delayed time plays an important role in MFPTs. Moreover, MFPT [Formula: see text] (stands for the Brownian particle moving from the left well to the middle well) is greater than [Formula: see text] (stands for the Brownian particle moving from the middle well to the left one).

Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning

Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing down, are ubiquitous in nonequilibrium systems such as supercooled liquids, amorphous solids, active matter, and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case or simply a crossover and even more so to measure the associated critical exponents. Here we show that the simulation results of a hard-sphere glass in three dimensions are consistent with the recent theoretical prediction of a Gardner transition, a continuous nonequilibrium phase transition. Using a hybrid molecular simulation-machine learning approach, we obtain scaling laws for both finite-size and aging effects and determine the critical exponents that traditional methods fail to estimate. Our study provides an approach that is useful to understand the nature of glass transitions and can be generalized to analyze other nonequilibrium phase transitions.

Topological defects as relics of spontaneous symmetry breaking from black hole physics

Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in strongly coupled systems, in absence of quasiparticles, is especially challenging. We investigate breaking of U(1) symmetry and the resulting spontaneous formation of vortices in a (2 + 1)-dimensional holographic superconductor employing gauge/gravity duality, a ‘first-principles’ approach to study strongly coupled systems. Magnetic fluxons with quantized fluxes are seen emerging in the post-transition superconducting phase. As expected in type II superconductors, they are trapped in the cores of the order parameter vortices. The dependence of the density of these topological defects on the quench time, the dispersion of the typical winding numbers, and the vortex-vortex correlations are consistent with predictions of the Kibble-Zurek mechanism.

Dissipative Josephson effect in coupled nanolasers

Josephson effects are commonly studied in quantum systems in which dissipation or noise can be neglected or do not play a crucial role. In contrast, here we discuss a setup where dissipative interactions do amplify a photonic Josephson current, opening a doorway to dissipation-enhanced sensitivity of quantum-optical interferometry devices. In particular, we study two coupled nanolasers subjected to phase coherent drivings and coupled by a coherent photon tunneling process. We describe this system by means of a Fokker–Planck equation and show that it exhibits an interesting non-equilibrium phase diagram as a function of the coherent coupling between nanolasers. As we increase that coupling, we find a non-equilibrium phase transition between a phase-locked (PL) and a non-phase-locked (NPL) steady-state, in which phase coherence is destroyed by the photon tunneling process. In the coherent, PL regime, an imbalanced photon number population appears if there is a phase difference between the nanolasers, which appears in the steady-state as a result of the competition between competing local dissipative dynamics and the Josephson photo-current. The latter is amplified for large incoherent pumping rates and it is also enchanced close to the lasing phase transition. We show that the Josephson photocurrent can be used to measure optical phase differences. In the quantum limit, the accuracy of the two nanolaser interferometer grows with the square of the photon number and, thus, it can be enhanced by increasing the rate of incoherent pumping of photons into the nanolasers.

Kinetic Control of Long‐Range Cationic Ordering in the Synthesis of Layered Ni‐Rich Oxides

AbstractDeciphering the sophisticated interplay between thermodynamics and kinetics of high‐temperature lithiation reaction is fundamentally significant for designing and preparing cathode materials. Here, the formation pathway of Ni‐rich layered ordered LiNi0.6Co0.2Mn0.2O2 (O‐LNCM622O) is carefully characterized using in situ synchrotron radiation diffraction. A fast nonequilibrium phase transition from the reactants to a metastable disordered Li1−x(Ni0.6Co0.2Mn0.2)1+xO2 (D‐LNCM622O, 0 < x < 0.95) takes place while lithium/oxygen is incorporated during heating before the generation of the equilibrium phase (O‐LNCM622O). The time evolution of the lattice parameters for layered nonstoichiometric D‐LNCM622O is well‐fitted to a model of first‐order disorder‐to‐order transition. The long‐range cation disordering parameter, Li/TM (TM = Ni, Co, Mn) ion exchange, decreases exponentially and finally reaches a steady‐state as a function of heating time at selected temperatures. The dominant kinetic pathways revealed here will be instrumental in achieving high‐performance cathode materials. Importantly, the O‐LNCM622O tends to form the D‐LNCM622O with Li/O loss above 850 °C. In situ XRD results exhibit that the long‐range cationic (dis)ordering in the Ni‐rich cathodes could affect the structural evolution during cycling and thus their electrochemical properties. These insights may open a new avenue for the kinetic control of the synthesis of advanced electrode materials.

Phase-space methods for simulating the dissipative many-body dynamics of collective spin systems

We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.

Magnetic Microswimmers Exhibit Bose-Einstein-like Condensation.

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of nonequilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a nonequilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical nonequilibrium phases of matter with traits that are analogous to those observed in quantum systems.

Modeling the evolution of drinking behavior: A Statistical Physics perspective

In this work we study a simple compartmental model for drinking behavior evolution. The population is divided in 3 compartments regarding their alcohol consumption, namely Susceptible individuals S (nonconsumers), Moderate drinkers M and Risk drinkers R. The transitions among those states are ruled by probabilities. Despite the simplicity of the model, we observed the occurrence of two distinct nonequilibrium phase transitions to absorbing states. One of these states is composed only by Susceptible individuals S, with no drinkers (M=R=0). On the other hand, the other absorbing state is composed only by Risk drinkers R (S=M=0). Between these two steady states, we have the coexistence of the three subpopulations S, M and R. Comparison with abusive alcohol consumption data for Brazil shows a good agreement between the model’s results and the database.

Numerical simulation of liquid CO2 accidental release at atmospheric environment

Investigation of the transient behaviour of high-pressure CO2 sudden release is important for the pipeline transportation safety of carbon capture and storage technology. A CFD model based on the volume of fluid method and non-equilibrium phase transition is established to simulate the high-pressure liquid CO2 release at atmospheric environment, which considers the flow domain out of the opening. The pressure drop and decompression wave speed predicted by CFD are in good agreement with the “shock tube” test results, which verifies the established CFD model. On this basis, we further investigate the transient behaviour of liquid CO2 release. The results show that the liquid-gas two-phase flow continues expanding outward from the rupture opening and sucking up the surrounding air, forming a complex three-phase under-expanded jet. It is found that the distance from rupture opening to Mach disk increases with the increase of initial pressure. It is also found that the liquid-gas CO2 mixture spurted from the rupture opening is mainly composed of liquid CO2 and a small amount of gaseous CO2 by analyzing the mass flow composition. Moreover, The static pressure and the total mass flow at the rupture opening both increase with the increase of the initial pressure, while the mass flow of the gas CO2 decreases with the increase of the initial pressure.

A CFD computational model for high-pressure liquid CO2 decompression

A CFD decompression model with considering external flow field is established based on the non-equilibrium phase transition. The results of pressure and decompression wave speed calculated by CFD are compared with the results of “shock tube” test, showing good agreement. On this basis, the effects of external flow field on the transient behaviour of liquid CO2 decompression in the pipe is further investigated. It is found that the external flow field basically has no effect on the variation of pressure and decompression wave speed in the pipe. Moreover, a Mach disk is formed at about 7.35R (R is the radius of rupture opening, 19.05 mm) away from the rupture opening in the process of jet expansion. Although the external flow field has a significant influence on the static pressure at the rupture opening, the mass flow in the case without considering external flow field is larger than that with considering external flow field, and the overall difference between the two cases is within 6%.

Model of Formation of Discrete Dislocations of the Thermoelastic Martensitic Transformation

The problem of the transition of a pre-martensite nanostructure of a SME crystal to a structure of discrete dislocation loops of the martensitic transformation is considered in the framework of the Ginzburg–Landau (GL) theory of nonequilibrium first-order phase transitions and a number of reasonable assumptions for the first time. Two asymptotic solutions of the GL equation have been obtained: one solution for a homogeneous source of crystal nanomodulation and another, for a spatially periodic pre-martensite nanostructure. An analysis of these solutions shows that the consolidation of local elastic lines of the nanostructure can be a cause of the formation of discrete dislocation loops of the martensitic transformation.

Role of compensating current in the weak Josephson coupling regime: An extended study on excitonic Josephson junctions

Huang's experiment [Phys. Rev. Lett. $\bf 109$, 156802 (2012)] found, in the quantum Hall bilayer of the Corbino geometry, the interlayer tunneling currents at two edges are coupled to each other and one of two tunneling currents is referred to as the compensating current of the other. Our another work[arXiv:2006.15329] has explained this exotic coupling phenomenon as a result of excitonic Josephson effect induced by interlayer tunneling current. In this paper, we study the same setup -- excitonic Josephson junction -- but in the weak Josephson coupling regime, which occurs for large junction length. Interestingly, we find the compensating current drives the other edge to undergo a nonequilibrium phase transition from a superfluid to resistive state, which is signaled by an abrupt jump of the critical tunneling current. We also identify the critical exponent and furthermore offer more experimental prediction.

Divalent Cations Induce Non-Equilibrium Phase Transitions in Tau-Mediated Microtubule Bundles Undergoing Dynamic Instability

The microtubule-associated protein tau is known for its ability to alter microtubule (MT) dynamic instability in developing and mature neurons and for its role in the pathology of many neurodegenerative diseases. Bundling of MTs into linear arrays (i.e. MT fascicles) is thought to be a cardinal feature of the axon initial segment of neurons, and tau's role in mediating MT-MT interactions in these arrays is thought to be critical for neuron function; however, the exact mechanism by which tau links and dictates the wide spacing of bundled MTs remains unclear. To help elucidate the nature of tau's role in physiological bundling of MTs, we have expanded on a recent platform for studying paclitaxel-free in vitro reaction mixtures of tubulin, GTP, and wild-type tau under dissipative, out-of-equilibrium conditions at 37 C. Using synchrotron small-angle x-ray scattering and transmission electron microscopy, we show that Ca2+ or Mg2+ in the mM concentration range can induce changes in the assembly of tubulin structures, revealing a phase transition between the previously reported widely spaced bundles and a novel transient bundled state with intermediate spacing. The latter bundled state is followed by rapid MT depolymerization and the formation of tubulin oligomers and rings. The transitions between each of these phases and their dependence on both time and cation concentration will be discussed.