Nonequilibrium Transition Research Articles

Irreversibility and Biased Ensembles in Active Matter: Insights from Stochastic Thermodynamics

Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained individual motion. It can lead to collective effects without any equilibrium equivalent, some of which can be rationalized by using equilibrium tools to recapitulate nonequilibrium transitions. An important challenge is then to delineate systematically to what extent the character of these active transitions is genuinely distinct from equilibrium analogs. We review recent works that use stochastic thermodynamics tools to identify, for active systems, a measure of irreversibility comprising a coarse-grained or informatic entropy production. We describe how this relates to the underlying energy dissipation or thermodynamic entropy production, and how it is influenced by collective behavior. Then, we review the possibility of constructing thermodynamic ensembles out of equilibrium, where trajectories are biased toward atypical values of nonequilibrium observables. We show that this is a generic route to discovering unexpected phase transitions in active matter systems, which can also inform their design.

Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits

Measurement-induced entanglement transitions in quantum dynamics represent a new class of nonequilibrium transitions, akin to thresholds in quantum error correction. In this work, the authors explore the universal properties of entanglement transitions in one- and two-dimensional monitored Clifford circuits, using a graph-state-based algorithm to unravel geometric properties of entanglement. A study of entanglement clusters in the steady state reveals that, despite similarities in the bulk, the surface critical exponents show strong deviations from classical percolation.

Antivax movement and epidemic spreading in the era of social networks: Nonmonotonic effects, bistability, and network segregation.

In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders-rather than favoring-the global disease spreading. Thus our results hint vaccination campaigns should avoid policies that end up segregating excessively antivaccine groups so that they effectively work as echo chambers in which individuals look to confirmation without jeopardizing the safety of the whole population.

Research on the influence of deformable sheet aluminum alloy rheological behavior on stretch forming process limits

Our research was aimed at modeling a symmetrical wrapping and stable control of the processes of shaping by wrapping a sheet blank along a wrapping punch having a double curvature surface and placed on the table of a virtual stretch-tightening press. The main task of modeling was to determine the deformed state with a uniform change in thickness in different regions of the sheet blank without folds and breaks, but without the influence of the rheological behavior of the deformable aluminum alloy. Here, the LS-DYNA software package is used with the use of an explicit or implicit solver for nonlinear problems of solid mechanics, characteristic of nonequilibrium transitions of the initial dissipative phase due to viscosity and heat transfer. Now it is possible to predict defect formation from a practical point of view, using the forming limit diagram (FLD), which makes it possible with sufficient accuracy to determine the degree of deformation of a given sheet material, at which any defects do not occur. The presented results of the study revealed the features of the influence of the rheological behavior of a wrought sheet aluminum alloy on the limits of the shaping process by a wrap.

Linear response in large deviations theory: a method to compute non-equilibrium distributions

We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scale-independent rate function (i.e. a large deviations principle is satisfied). In order to provide an explicit expression for the probability distribution valid away from equilibrium, we propose a linear response theory performed at the level of the rate function. We show that the first order non-equilibrium contribution to the steady state rate function, g( x ), satisfies where the vector field u ( x ) defines the macroscopic deterministic dynamics, and the scalar field equals the rate at which work is performed on the system in a given state x . This equation provides a practical way to determine g( x ), significantly outperforms standard linear response theory applied at the level of the probability distribution, and approximates the rate function surprisingly well in some far-from-equilibrium conditions. The method applies to a wealth of physical and chemical systems, that we exemplify by two analytically tractable models—an electrical circuit and an autocatalytic chemical reaction network—both undergoing a non-equilibrium transition from a monostable phase to a bistable phase. Our approach can be easily generalized to transient probabilities and non-autonomous dynamics. Moreover, its recursive application generates a virtual flow in the probability space which allows to determine the steady state rate function arbitrarily far from equilibrium.

High-Pressure Nonequilibrium Dynamics on Second-to-Microsecond Time Scales: Application of Time-Resolved X-ray Diffraction and Dynamic Compression in Ice.

The study of nonequilibrium transition dynamics on structural transformation from the second to microsecond regime, a time scale between static and shock compression, is an emerging field of high-pressure research. There are ample opportunities to uncover novel physical phenomena within this time regime. Herein, we briefly review the development and application of a dynamic compression technique based on a diamond anvil cell (DAC) and time-resolved X-ray diffraction (TRXRD) for the study of time-, pressure-, and temperature-dependent structural dynamics. Applications of the techniques are illustrated with our recent investigations on the mechanisms of the interconversions between different high-pressure ice polymorphs. These examples demonstrate that a combination of dynamic compression and TRXRD is a versatile approach capable of providing information on the kinetics and thermodynamic nature associated with structural transformations. Future improvement of rapid compression and TRXRD techniques and potentially interesting research topics in this area are suggested.

Mechanical Regulation of Epithelial Tissue Homeostasis

Despite recent efforts to understand homeostasis in epithelial tissues, there are many unknowns surrounding this steady state. It is considered to be regulated by mechanoresponse, but unlike for single cells, this idea remains heavily debated for tissues. Here, we show that changes in matrix stiffness induce a nonequilibrium transition from tubular to squamous Madin-Darby Canine Kidney II tissues. Nonetheless, despite different cell morphologies and densities, all homeostatic tissues display equivalent topologies, which, hence, must be actively targeted and regulated. On the contrary, the mechanoresponse induces dramatic changes in the large-scale organization of the colonies. On stiff gels, this yields an unreported cooperative state of motile cells displaying higher densities than in the arrested homeostatic state, which suggests a more complex relation between cell density and motility than previously anticipated. Our results unequivocally relate the mechanosensitive properties of individual cells to the evolving macroscopic structures, an effect that could be important for understanding the emergent pathologies of living tissues.12 MoreReceived 27 August 2020Revised 18 March 2021Accepted 26 May 2021Corrected 18 August 2021DOI:https://doi.org/10.1103/PhysRevX.11.031029Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCell mechanicsPhysical SystemsEpithelial cellsTechniquesDissipative particle dynamicsBiological Physics

Continuous nonequilibrium transition driven by heat flow

We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states.

Dynamical ordering in a two-dimensional electron crystal confined in a narrow channel geometry

We present both time-averaged and time-resolved transport measurements of a two-dimensional electron (Wigner) crystal on the surface of superfluid helium confined in a narrow microchannel. We find that the field-current characteristics of the driven crystal obtained by the time-averaged measurements exhibit oscillations and negative differential conductivity. This unusual transport behavior was observed previously by Glasson et al. [Phys. Rev. Lett. 87, 176802 (2001)] and was attributed to a nonequilibrium transition of the electron system to a novel dynamically ordered phase of current filaments aligned along the channels. Contrarily to this explanation, our time-resolved transport measurements reveal that oscillating field-current characteristics appear due to dynamical decoupling (slipping) and recoupling (sticking) of the uniform electron crystal to the liquid helium substrate. Our result demonstrates that this unusual non-linear transport effect is intrinsic, does not depend on the device geometry, and is associated with the dynamical interaction of Wigner crystal with the surface excitations of the liquid substrate.

Noise-induced symmetry breaking of self-regulators: Nonequilibrium transition toward homochirality.

We present a theoretical model to study the origin of chiral symmetry breaking of a racemic mixture of optically active biomolecules. We consider a collection of Brownian particles, which can stay in any of the three possible isomeric states: one achiral and two enantiomers. Isomers are undergoing self-regulatory reaction along with chiral inhibition and achiral decay processes. The reaction rates of the isomeric states are guided by their neighbors as well as the thermal fluctuations of the system. We find that an alteration in the relative dominance of self-regulation, chiral inhibition, and achiral decay processes breaks the chiral symmetry of the system, which is either partial or complete. This results in four different asymmetric population states, viz., three-isomer coexistence, enantiomeric coexistence, chiral-achiral coexistence, and homochiral state. A change in the reaction condition induces nonequilibrium transition among these states. We also report that a fast stochastic self-regulation and a slow chiral inhibition and achiral decay process along with a threshold population of interacting neighbors suffice for the requisite for transition toward a completely symmetry broken state, i.e., homochirality.

Transport and fluctuations in mass aggregation processes: Mobility-driven clustering.

We calculate the bulk-diffusion coefficient and the conductivity in nonequilibrium conserved-mass aggregation processes on a ring. These processes involve chipping and fragmentation of masses, which diffuse on a lattice and aggregate with their neighboring masses on contact, and, under certain conditions, they exhibit a condensation transition. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility of masses, is greatly enhanced. The enhancement in the conductivity, in accordance with the Einstein relation, results in large mass fluctuations and can induce a mobility-driven clustering in the systems. Indeed, in a certain parameter regime, we show that the conductivity, along with the mass fluctuation, diverges beyond a critical density, thus characterizing the previously observed nonequilibrium condensation transition [Phys. Rev. Lett. 81, 3691 (1998)10.1103/PhysRevLett.81.3691] in terms of an instability in the conductivity. Notably, the bulk-diffusion coefficient remains finite in all cases. We find our analytic results in quite good agreement with simulations.

Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure

Persistent dynamics in colloidal glasses suggest the existence of a non-equilibrium driving force for structural relaxation during glassy aging. But the implicit assumption in the literature that colloidal glasses form within the metastable state bypasses the search for a driving force for vitrification and glassy aging and its connection with a metastable state. The natural relation of osmotic pressure to number-density gradients motivates us to investigate the osmotic pressure as this driving force. We use dynamic simulation to quench a polydisperse hard-sphere colloidal liquid into the putative glass region while monitoring structural relaxation and osmotic pressure. Following quenches to various depths in volume fraction ϕ (where ϕ RCP ≈ 0.678 for 7% polydispersity), the osmotic pressure overshoots its metastable value, then decreases with age toward the metastable pressure, driving redistribution of coordination number and interparticle voids that smooths structural heterogeneity with age. For quenches to 0.56 ⩽ ϕ ⩽ 0.58, accessible post-quench volume redistributes with age, allowing the glass to relax into a strong supercooled liquid and easily reach a metastable state. At higher volume fractions, 0.59 ⩽ ϕ < 0.64, this redistribution encounters a barrier that is subsequently overcome by osmotic pressure, allowing the system to relax toward the metastable state. But for ϕ ⩾ 0.64, the overshoot is small compared to the high metastable pressure; redistribution of volume stops as particles acquire contacts and get stuck, freezing the system far from the metastable state. Overall, the osmotic pressure drives structural rearrangements responsible for both vitrification and glassy age-relaxation. The connection of energy, pressure, and structure identifies the glass transition, 0.63 < ϕ g ⩽ 0.64. We leverage the connection of osmotic pressure to energy density to put forth the mechanistic view that relaxation of structural heterogeneity in colloidal glasses occurs via individual particle motion driven by osmotic pressure, and is a spontaneous energy minimization process that drives the glass off and back to the metastable state.

Dynamic Instability from Non-Equilibrium Structural Transitions on the Energy Landscape of Microtubule

Microtubules are the backbone of the cytoskeleton and vital to numerous cellular processes. The central dogma of microtubules is that all their functions are driven by dynamic instability, but its mechanism has remained unresolved for over thirty years due to conceptual difficulties inherent in the dominant GTP-cap framework. We present a physically rigorous structural mechano-chemical model: dynamic instability is driven by non-equilibrium transitions between the bent (B), straight (S) and curved (C) forms of tubulin monomers and longitudinal interfaces in the two-dimensional lattice of microtubule. All the different phenomena (growth, shortening, catastrophe, rescue and pausing) are controlled by the kinetic pathways for transitions and corresponding energy landscapes. Different kinetics at minus-end are due to different pathways imposed by the polarity of microtubule lattice. This model enables us to reproduce all the observed phenomena of dynamic instability of purified tubulins in kinetic simulations.

Nonequilibrium multiple transitions in the core-shell Ising nanoparticles driven by randomly varying magnetic fields

The nonequilibrium behaviour of a core-shell nanoparticle has been studied by Monte-Carlo simulation. The core consists of Ising spins of σ=1/2 and the shell contains Ising spins of S=1. The interactions within the core and in the shell are considered ferromagnetic but the interfacial interaction between core and shell is antiferromagnetic. The nanoparticle system is kept in open boundary conditions and is driven by randomly varying (in time but uniform over the space) magnetic field. Depending on the width of the randomly varying field and the temperature of the system, the core, shell and total magnetization varies in such a manner that the time averages vanish for higher magnitude of the width of random field, exhibiting a dynamical symmetry breaking transitions. The susceptibilities get peaked at two different temperatures indicating nonequilibrium multiple transitions. The phase boundaries of the nonequilibrium multiple transitions are drawn in the plane formed by the axes of temperature and the width of the randomly varying field. Furthermore, the effects of the core and shell thicknesses on the multiple transitions have been discussed.

Dynamic Instability from Non-equilibrium Structural Transitions on the Energy Landscape of Microtubule.

Microtubules are the backbone of the cytoskeleton and vital to numerous cellular processes. The central dogma of microtubules is that all their functions are driven by dynamic instability, but its mechanism has remained unresolved for over 30 years because of conceptual difficulties inherent in the dominant GTP-cap framework. We present a physically rigorous structural mechanochemical model: dynamic instability is driven by non-equilibrium transitions between the bent (B), straight (S), and curved (C) forms of tubulin monomers and longitudinal interfaces in the two-dimensional lattice of microtubule. All the different phenomena (growth, shortening, catastrophe, rescue, and pausing) are controlled by the kinetic pathways for B↔S↔C transitions and corresponding energy landscapes. Different kinetics at minus end are due to different B↔S↔C pathways imposed by the polarity of microtubule lattice. This model enables us to reproduce all the observed phenomena of dynamic instability of purified tubulins in kinetic simulations.

Emergent solidity of amorphous materials as a consequence of mechanical self-organisation

Amorphous solids have peculiar properties distinct from crystals. One of the most fundamental mysteries is the emergence of solidity in such nonequilibrium, disordered state without the protection by long-range translational order. A jammed system at zero temperature, although marginally stable, has solidity stemming from the space-spanning force network, which gives rise to the long-range stress correlation. Here, we show that such nonlocal correlation already appears at the nonequilibrium glass transition upon cooling. This is surprising since we also find that the system suffers from giant anharmonic fluctuations originated from the fractal-like potential energy landscape. We reveal that it is the percolation of the force-bearing network that allows long-range stress transmission even under such circumstance. Thus, the emergent solidity of amorphous materials is a consequence of nontrivial self-organisation of the disordered mechanical architecture. Our findings point to the significance of understanding amorphous solids and nonequilibrium glass transition from a mechanical perspective.

Application of temperature modulation to FTIR spectroscopy: an analysis of equilibrium and non-equilibrium conformational transitions of poly(ethylene terephthalate) in glassy and liquid states

In this paper, the application of a temperature modulation to the temperature-resolved FTIR analysis is reported. The advantage offered by the spectroscopic investigation, able to follow the micro-structural and conformational sample modification involved in sample thermal transformation, was merged to that of temperature modulation, related to the possibility to separate the reversing (in-equilibrium within the experimental condition) to the non-reversing (non-equilibrium) processes. The potentiality of the technique (modulated temperature FTIR, MTFTIR) is highlighted through the study of the thermal transitions of amorphous poly(ethylene terephthalate) from 50 °C to the cold-crystallization. After the presentation of the theoretical framework and the experimental conditions, a step-by-step description of acquired data elaboration is given. The total variation of a selected band intensity as function of mean temperature as well as its reversing and non-reversing components are obtained. The evolution of the bands at 1340 and 971 cm−1, assigned to the trans conformation of the ethylenic unit and to the all-trans conformation of the repeating unit, respectively, are investigated. As expected, the glass transition is observed in the reversing components meanwhile the recovery of the glass relaxation and cold crystallization in non-reversing ones. Particularly interesting resulted the behaviour of the sample in the supercooled liquid state, between the glass transition and the cold-crystallization onset, in which the results show that the ethylenic conformers are in-equilibrium while the all-trans sequences are not. MTFTIR is confirmed to be a technique particularly suitable for the characterization of non-equilibrium conformational states of polymers.

Study of the Dusty-Gas Discharge Plasma in the Plasma Crystal-3 Plus Space Laboratory (Review)

The main results of a completed cycle of complex studies of a strongly coupled dusty plasma conducted in the unique, experimental Plasma Crystal-3 Plus space laboratory that operated on the International Space Station are discussed. The experiments on the physics of phenomena in the dusty plasma are analyzed. A new state of dusty plasma, the electrorheological plasma, in which there is a transition from an isotropic plasma-dusty liquid to an anisotropic state, is studied. The study of the interpenetration of particles streams of various diameters, a nonequilibrium transition, is described. Experimental studies of the liquid–crystal phase transition in a three-dimensional dusty plasma system in which it is established that the dust component is compressed and crystallized upon a decrease in the neutral gas pressure are discussed. The nearly free motion of large particles in the volume of a plasma crystal, a nonviscous, irrotational flow about a large particle by a “liquid” of small dust particles, is analyzed. An experimental study of the dynamics of the crystallization of three-dimensional plasma-dust systems at a constant argon pressure under the effect of a low-frequency, alternating electric field and without its influence under microgravity conditions is described. The formation of the crystallization front and its propagation in the three-dimensional plasma-dust system with a velocity on the order of the average interparticle distance per second were discovered.

Synchronization and fluctuations: Coupling a finite number of stochastic units.

It is well established that ensembles of globally coupled stochastic oscillators may exhibit a nonequilibrium phase transition to synchronization in the thermodynamic limit (infinite number of elements). In fact, since the early work of Kuramoto, mean-field theory has been used to analyze this transition. In contrast, work that directly deals with finite arrays is relatively scarce in the context of synchronization. And yet it is worth noting that finite-number effects should be seriously taken into account since, in general, the limits N→∞ (where N is the number of units) and t→∞ (where t is time) do not commute. Mean-field theory implements the particular choice first N→∞ and then t→∞. Here we analyze an ensemble of three-state coupled stochastic units, which has been widely studied in the thermodynamic limit. We formally address the finite-N problem by deducing a Fokker-Planck equation that describes the system. We compute the steady-state solution of this Fokker-Planck equation (that is, finite N but t→∞). We use this steady state to analyze the synchronic properties of the system in the framework of the different order parameters that have been proposed in the literature to study nonequilibrium transitions.

Role of fluctuations in the yielding transition of two-dimensional glasses

We numerically study yielding in two-dimensional glasses which are generated with a very wide range of stabilities by swap Monte-Carlo simulations and then slowly deformed at zero temperature. We provide strong numerical evidence that stable glasses yield via a nonequilibrium discontinuous transition in the thermodynamic limit. A critical point separates this brittle yielding from the ductile one observed in less stable glasses. We find that two-dimensional glasses yield similarly to their three-dimensional counterparts but display larger sample-to-sample disorder-induced fluctuations, stronger finite-size effects, and rougher spatial wandering of the observed shear bands. These findings strongly constrain effective theories of yielding.