First-order phase transition in a model glass former: coupling of local structure and dynamics

Parking spheres stochastically to model realistic granular packings

The packing geometry of granular solids and other amorphous materials is important to understand their macroscopic behaviors. However, their particle-scale assembly mechanism and the underlying statistical mechanical laws remain unclear. In this work, we develop a model to generate the local packing structures of granular spheres by parking them sequentially and stochastically, and connect the fluctuating structures to the thermodynamic equations of state. The influences of entropy, friction, and mechanical action on local configurations are decomposed with the aid of an effective interparticle interaction, a parking sequence of neighboring particles, and an external potential. Quasiuniversal laws of granular sphere packings observed in previous experiments are replicated by our model and their empirical dependences on particle friction and packing protocol are rationalized. This model provides a general statistical mechanical approach to understanding the nonequilibrium assembly mechanism of amorphous particle packing systems.

Structural Origin of Dynamic Heterogeneity in Supercooled Liquids

As a liquid is supercooled toward the glass transition point, its dynamics slow significantly, provided that crystallization is avoided. With increased supercooling, the particle dynamics become more spatially heterogeneous, a phenomenon known as dynamic heterogeneity. Since its discovery, this characteristic of metastable supercooled liquids has garnered considerable attention in glass science. However, the precise physical origins of dynamic heterogeneity remain elusive and widely debated. In this perspective, we examine the relationship between dynamic heterogeneity and structural order, based on numerical simulations of fragile liquids with isotropic potentials and strong liquids with directional interactions. We demonstrate that angular ordering, arising from many-body steric interactions, plays a crucial role in the slow dynamics and dynamic cooperativity of fragile liquids. Additionally, we explore how the growth of static order correlates with slower dynamics. In fragile liquids exhibiting super-Arrhenius behavior, the spatial extent of regions with high angular order grows upon cooling, and the sequential propagation of particle rearrangements within these ordered regions increases the activation energy for particle motion. In contrast, strong liquids with spatially constrained local ordering display a distinct "two-state" dynamic characteristic, marked by a transition between two Arrhenius-type behaviors. We argue that dynamic heterogeneity, irrespective of a liquid's fragility, arises from underlying structural order, with its spatial extent determined by static ordering. This perspective aims to deepen our understanding of the interplay between structural and dynamic properties in metastable supercooled liquids.

Bringing Together Two Paradigms of Nonequilibrium: Fragile versus Robust Aging in Driven Glassy Systems

There are two key paradigms for nonequilibrium dynamics: on the one hand, aging toward an equilibrium state that cannot be reached on reasonable timescales; on the other, external driving that can lead to nonequilibrium steady states. We explore how these two mechanisms interact by studying the behavior of trap models, which are paradigmatic descriptions of slow glassy dynamics, when driven by trajectory bias toward high or low activity. To diagnose whether the driven systems continue to age, we establish a framework for mapping the biased dynamics to a Markovian time evolution with time-dependent transition rates. We find that the original aging dynamics reacts in two qualitatively distinct ways to the driving: it can be destroyed by the driving of any nonzero strength ("fragile" aging), whereby the dynamics either reaches an active steady state or effectively freezes, or it can persist within a finite range of driving strengths around the undriven case ("robust" aging). This classification into fragile and robust aging could form the basis for distinguishing different universality classes of aging dynamics.

Dynamical Phase Transition in Kinetically Constrained Models with Energy-Activity Double-Bias Trajectory Ensemble

We investigate the dynamical phase transitions in two representative kinetically constrained models, the 1D Fredrickson-Andersen and East models, by utilizing a recently developed s,g double-bias ensemble approach. In this ensemble, the fields s and g are applied to bias the dynamical activity and trajectory energy, respectively, in the trajectory ensemble. We first confirm that the dynamical phase transitions are indeed first-order in both the models. The phase diagrams in (s, g, T) space obtained via extensive numerical simulations show good qualitative agreement with the mean-field results. We also demonstrate that the temperature-dependent dynamical phase transition is possible in the systems when both fields are applied simultaneously. The trajectory energy and dynamical activity exhibit strong correlations for both systems. From extensive finite-size scaling analyses using the system size and observation time, we obtain scaling functions for the susceptibility and field and find scaling exponents that are model-dependent.

Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.

Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model

We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of [Formula: see text] non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin configurations with uniform rates. We show that the cumulant generating function of the time-integral of a normally distributed quenched random function of configurations, i.e. the energy function of the random energy model (REM), has a phase transition in the large [Formula: see text] limit for trajectories of any time extent. We prove this by determining the exact limit of the scaled cumulant generating function. This is accomplished by connecting the dynamical problem to a spectral analysis of the all-to-all quantum REM. We also discuss finite [Formula: see text] corrections as observed in numerical simulations. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions

For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have revealed that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that if we only consider the standard deviation from the expectation, any anomalous behavior will not be detected. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.

Reaction-path statistical mechanics of enzymatic kinetics

We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies by using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme-substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit.

Translation-rotation decoupling of tracers reflects medium-range crystalline order in two-dimensional colloid glasses

The dynamic heterogeneity and the translation-rotation decoupling are the dynamic signatures of glasses and supercooled liquids. Whether and how the dynamic heterogeneity would relate to the local structure of glasses has been a puzzle for decades. In this work we perform molecular dynamics simulations for tracers in both two-dimensional polydisperse colloids (2DPC) and two-dimensional binary colloids (2DBC). In 2DPC glasses, hexatic local structures develop at low enough temperatures and grow quickly along with the dynamic correlation length of the 2DPC, which is well known as the medium-range crystalline order (MRCO). In 2DBC glasses, on the other hand, any explicit local structure has not been reported to grow significantly with the dynamic correlation length at low temperatures. We introduce two different types of tracers into colloidal systems: A diamond tracer that resembles the MRCO of 2DPC glasses and a square tracer that is dissimilar to any local structure of glasses. The translation-rotation decoupling of the diamond tracer in 2DPC glasses is much more significant than that of the square tracer in the same 2DPC glasses. On the other hand, such a tracer shape-dependence of the decoupling is not observed in 2DBC glasses where the local hexatic structure does not develop significantly. We introduce a shape-dependency parameter of the decoupling and find that the shape-dependency parameter grows along with the dynamic correlation length in 2DPC glasses but not in 2DBC glasses. This illustrates that the dynamic heterogeneity and the translation-rotation decoupling of tracers could reveal the local structure that develops in glasses.

Isomorphs in nanoconfined liquids

We study in this paper the possible existence of Roskilde-simple liquids and their isomorphs in a rough-wall nanoconfinement. Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant in suitable nondimensionalized units. Two model liquids using molecular dynamics computer simulations are considered: the single-component Lennard-Jones (LJ) liquid and the Kob-Andersen binary LJ mixture, both of which in the bulk phases are known to have good isomorphs. Nanoconfinement is implemented by adopting a slit-pore geometry with fcc crystalline walls; this implies inhomogenous density profiles both parallel and perpendicular to the confining walls. Despite this fact and consistent with an earlier study [Ingebrigtsen et al., Phys. Rev. Lett., 2013, 111, 235901] we find that these two nanoconfined liquids have isomorphs to a good approximation. More specifically, we show good invariance along the isomorphs of inhomogenous density profiles, mean-square displacements, and higher-order structures probed using the topological cluster classification algorithm. Our study thus provides an alternative framework for understanding nanoconfined liquids.

Long-ranged correlations in large deviations of local clustering

In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realize large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyze this effect through the lens of macroscopic fluctuation theory, focusing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has nontrivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.

Collective motion in large deviations of active particles

We analyze collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyze the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.

Autonomously revealing hidden local structures in supercooled liquids

Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids. To explore this link, much research has been devoted to pinpointing local structures and order parameters that correlate strongly with dynamics. Here we use an unsupervised machine learning algorithm to identify structural heterogeneities in three archetypical glass formers—without using any dynamical information. In each system, the unsupervised machine learning approach autonomously designs a purely structural order parameter within a single snapshot. Comparing the structural order parameter with the dynamics, we find strong correlations with the dynamical heterogeneities. Moreover, the structural characteristics linked to slow particles disappear further away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.

The origin of dynamical slowdown in disordered materials remains elusive, especially in the absence of obvious structural changes. Boattini et al. use unsupervised machine learning to reveal correlations between structural and dynamical heterogeneity in supercooled liquids.

Dynamic phase transitions in freestanding polymer thin films

After more than two decades of study, many fundamental questions remain unanswered about the dynamics of glass-forming materials confined to thin films. Experiments and simulations indicate that free interfaces enhance dynamics over length scales larger than molecular sizes, and this effect strengthens at lower temperatures. The nature of the influence of interfaces, however, remains a point of significant debate. In this work, we explore the properties of the nonequilibrium phase transition in dynamics that occurs in trajectory space between high- and low-mobility basins in a set of model polymer freestanding films. In thick films, the film-averaged mobility transition is broader than the bulk mobility transition, while in thin films it is a variant of the bulk result shifted toward a higher bias. Plotting this transition's local coexistence points against the distance from the films' surface shows thick films have surface and film-center transitions, while thin films practically have a single transition throughout the film. These observations are reminiscent of thermodynamic capillary condensation of a vapor-liquid phase between parallel plates, suggesting they constitute a demonstration of such an effect in a trajectory phase transition in the dynamics of a structural glass former. Moreover, this transition bears similarities to several experiments exhibiting anomalous behavior in the glass transition upon reducing film thickness below a material-dependent onset, including the broadening of the glass transition and the homogenization of surface and bulk glass transition temperatures.

Hierarchical glass transition of hard hemidisks with local assemblies

Using computer simulation, we investigate the glass transition of a two-dimensional hard-hemidisk system. Upon increasing the packing fraction of the system, we find that the system vitrifies into a glass with local assembled discal "dimers", which are free to rotate in a collective way. The rotational mean square displacement does not exhibit the typical plateau (slowdown) like what occurs in the translational mean square displacement. This effect induces a pronounced violation of the rotational Stokes-Einstein relationship compared with the translational degree of freedom at the supercooled region. However, the obtained glass transition points in these two freedom degrees are found to be the same within the numerical accuracy, which is due to the strong positive spatial and dynamic correlation between translational and rotational slow-moving particles. Moreover, we find that the locally assembled dimers can serve as fast rotating gears facilitating the orientational relaxation in the system, and this suggests that the locally favored finite structures play an important role in the hierarchical glass transition of anisotropic colloids.

Dynamical phase transitions and their relation to structural and thermodynamic aspects of glass physics

We review recent developments in structural-dynamical phase transitions in trajectory space based on dynamic facilitation theory. An open question is how the dynamic facilitation perspective on the glass transition may be reconciled with thermodynamic theories that posit collective reorganization accompanied by a growing static length scale and, eventually, a vanishing configurational entropy. In contrast, dynamic facilitation theory invokes a dynamical phase transition between an active phase (close to the normal liquid) and an inactive phase, which is glassy and whose order parameter is either a time-averaged dynamic or structural quantity. In particular, the dynamical phase transition in systems with non-trivial thermodynamics manifests signatures of a lower critical point that lies between the mode-coupling crossover and the putative Kauzmann temperature, at which a thermodynamic phase transition to an ideal glass state would occur. We review these findings and discuss such criticality in the context of the low-temperature decrease in configurational entropy predicted by thermodynamic theories of the glass transition.

A deep learning functional estimator of optimal dynamics for sampling large deviations

In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to access these rare events is by means of an auxiliary dynamics obtained from the original one through the so-called ‘generalised Doob transformation’. While this optimal dynamics is guaranteed to exist its use is often impractical, as to define it requires the often impossible task of diagonalising a (tilted) dynamical generator. While approximate schemes have been devised to overcome this issue they are difficult to automate as they tend to require knowledge of the systems under study. Here we address this problem from the perspective of deep learning. We devise an iterative semi-supervised learning scheme which converges to the optimal or Doob dynamics with the clear advantage of requiring no prior knowledge of the system. We test our method in a paradigmatic statistical mechanics model with non-trivial dynamical fluctuations, the fully packed classical dimer model on the square lattice, showing that it compares favourably with more traditional approaches. We discuss broader implications of our results for the study of rare dynamical trajectories.

Trajectory phase transitions in noninteracting spin systems

We show that a collection of independent Ising spins evolving stochastically can display surprisingly large fluctuations toward ordered behavior, as quantified by certain types of time-integrated plaquette observables, despite the underlying dynamics being noninteracting. In the large-deviation (LD) regime of long times and large system size, this can give rise to a phase transition in trajectory space. As a noninteracting system we consider a collection of spins undergoing single spin-flip dynamics at infinite temperature. For the dynamical observables we study, the associated tilted generators have an exact and explicit spin-plaquette duality. Such setup suggests the existence of a transition (in the large size limit) at the self-dual point of the tilted generator. The nature of the LD transition depends on the observable. We consider explicitly two situations: (i) for a pairwise bond observable the LD transition is continuous and equivalent to that of the transverse field Ising model and (ii) for a higher-order plaquette observable, in contrast, the LD transition is first order. Case (i) is easy to prove analytically, while we confirm case (ii) numerically via an efficient trajectory sampling scheme that exploits the noninteracting nature of the original dynamics.

Using Matrix Product States to Study the Dynamical Large Deviations of Kinetically Constrained Models

Here we demonstrate that tensor network techniques-originally devised for the analysis of quantum many-body problems-are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples, we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modeling of glasses. We show how variational matrix product states allow us to numerically approximate-systematically and with high accuracy-the leading eigenstates of the tilted dynamical generators, which encode the large deviation statistics of the dynamics. Via this approach, we can study system sizes beyond what is possible with other methods, allowing us to characterize in detail the finite size scaling of the trajectory-space phase transition of these models, the behavior of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.

Physical swap dynamics, shortcuts to relaxation, and entropy production in dissipative Rydberg gases

Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.

Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit "Doob-transformed" dynamics that optimally realizes rare dynamical events.

Sampling rare events across dynamical phase transitions

Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. In some cases, this leads to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence. However, during the last decade, advanced computational techniques have been developed to measure rare events in simulations of many-particle systems that allow the direct observation and characterization of these DPTs. Here we review the application of a particular rare-event simulation technique, based on cloning Monte Carlo methods, to characterize DPTs in paradigmatic stochastic lattice gases. In particular, we describe in detail some tricks and tips of the trade, paying special attention to the measurement of order parameters capturing the physics of the different DPTs, as well as to the finite-size effects (both in the system size and in the number of clones) that affect the measurements. Overall, we provide a consistent picture of the phenomenology associated with DPTs and their measurement.

The race to the bottom: approaching the ideal glass?

Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.

Glass forming phase diagram and local structure of Kob-Andersen binary Lennard-Jones nanoparticles

Molecular dynamics simulation is used to study glass formation in Kob-Andersen binary Lennard-Jones nanoparticles and determine the glass forming phase diagram for the system as a function of composition. The radial distribution function, a Steinhardt bond-orientational order parameter, and favored local structure analysis are used to distinguish between glassy and ordered systems. We find that surface enrichment of the large atoms alters the nanoparticle core composition, leading to an overall shift of the glass forming region to lower small atom mole fractions, relative to the bulk system. At small atom mole fraction, x_B = 0.1, the nanoparticles form a solid with an amorphous core, enriched with the small atoms, surrounded by a partially ordered surface region, enriched with the large atom component. The most disordered glass nanoparticles occur at x_B ≈ 0.3, but the surface-core enrichment leads to the crystallization of the nanoparticle to the CsCl crystal above x_B ≈ 0.35, which is lower than observed in the bulk. The glass transition temperatures of the nanoparticles are also significantly reduced. This allows the liquid to remain dynamic to low temperatures and sample the low energy inherent structure minima on the potential energy surface containing a high abundance of favoured local structures.

Weak temperature dependence of ageing of structural properties in atomistic model glassformers

Ageing phenomena are investigated from a structural perspective in two binary Lennard-Jones glassformers, the Kob-Andersen and Wahnström mixtures. In both, the geometric motif assumed by the glassformer upon supercooling, the locally favoured structure (LFS), has been established. The Kob-Andersen mixture forms bicapped square antiprisms; the Wahnström model forms icosahedra. Upon ageing, we find that the structural relaxation time has a time-dependence consistent with a power law. However, the LFS population and potential energy increase and decrease, respectively, in a logarithmic fashion. Remarkably, over the time scales investigated, which correspond to a factor of 10⁴ change in relaxation times, the rate at which these quantities age appears almost independent of temperature. Only at temperatures far below the Vogel-Fulcher-Tamman temperature do the ageing dynamics slow.

Structural-dynamical transition in the Wahnström mixture

In trajectory space, dynamical heterogeneities in glass-forming liquids correspond to the emergence of a dynamical phase transition between an active phase poor in local structure and an inactive phase which is rich in local structure. We support this scenario with the study of a model additive mixture of Lennard-Jones particles, quantifying how the choice of the relevant structural and dynamical observable affects the transition in trajectory space. We find that the low mobility, structure-rich phase is dominated by icosahedral order. Applying a non-equilibrium rheological protocol, we connect local order to the emergence of mechanical rigidity.

Lee-Yang zeros and large-deviation statistics of a molecular zipper

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems. Today, Lee-Yang zeros are no longer just a theoretical concept; they have been determined in recent experiments. In one approach, the Lee-Yang zeros are extracted from the high cumulants of thermodynamic observables at finite size. Here we employ this method to investigate a phase transition in a molecular zipper. From the energy fluctuations in small zippers, we can predict the temperature at which a phase transition occurs in the thermodynamic limit. Even when the system does not undergo a sharp transition, the Lee-Yang zeros carry important information about the large-deviation statistics and its symmetry properties. Our work suggests an interesting duality between fluctuations in small systems and their phase behavior in the thermodynamic limit. These predictions may be tested in future experiments.

Order and Symmetry Breaking in the Fluctuations of Driven Systems

Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time a DPT in the current vector statistics of an archetypal two-dimensional (2D) driven diffusive system and characterize its properties using the macroscopic fluctuation theory. The complex interplay among the external field, anisotropy, and vector currents in 2D leads to a rich phase diagram, with different symmetry-broken fluctuation phases separated by lines of first- and second-order DPTs. Remarkably, different types of 1D order in the form of jammed density waves emerge to hinder transport for low-current fluctuations, revealing a connection between rare events and self-organized structures which enhance their probability.

Experimental Evidence for a Structural-Dynamical Transition in Trajectory Space

Among the key insights into the glass transition has been the identification of a nonequilibrium phase transition in trajectory space which reveals phase coexistence between the normal supercooled liquid (active phase) and a glassy state (inactive phase). Here, we present evidence that such a transition occurs in experiments. In colloidal hard spheres, we find a non-Gaussian distribution of trajectories leaning towards those rich in locally favored structures (LFSs), associated with the emergence of slow dynamics. This we interpret as evidence for a nonequilibrium transition to an inactive LFS-rich phase. Reweighting trajectories reveals a first-order phase transition in trajectory space between a normal liquid and a LFS-rich phase. We also find evidence for a purely dynamical transition in trajectory space.

Experimental Determination of Dynamical Lee-Yang Zeros

Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros-complex singularities of the free energy in systems of finite size-have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize nonequilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for determining Lee-Yang zeros in such nonequilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From the short-time behavior of the Lee-Yang zeros, we predict the large-deviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

Structure in sheared supercooled liquids: Dynamical rearrangements of an effective system of icosahedra

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of particles organized into icosahedra under simple steady state shear. We recast this glassformer as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)]. From the observed population of icosahedra in each steady state, we obtain an effective temperature which is linearly dependent on the shear rate in the range considered. Upon shear banding, the system separates into a region of high shear rate and a region of low shear rate. The effective temperatures obtained in each case show that the low shear regions correspond to a significantly lower temperature than the high shear regions. Taking a weighted average of the effective temperature of these regions (weight determined by region size) yields an estimate of the effective temperature which compares well with an effective temperature based on the global mesocluster population of the whole system.

The role of fivefold symmetry in suppressing crystallization

Although long assumed to have an important role in the suppression of crystallization and the development of glassformers, the effect of local fivefold symmetry has never been directly tested. Here we consider whether such suppression of crystallization has a kinetic or thermodynamic nature and investigate its mechanism. We introduce a model in which the degree of fivefold symmetry can be tuned by favouring arrangements of particles in pentagonal bipyramids. We thus show that fivefold symmetry has both kinetic and thermodynamic effects on the mechanism of crystallization to a face-centred cubic crystal. Our results suggest that the mechanism of crystallization suppression is related to the surface tension between fluid and crystal. Interestingly, the degree of fivefold symmetry has little effect on crystal growth rate, suggesting that growth may be only weakly coupled to fluid structure in hard sphere like systems. Upon increasing the fivefold symmetry, we find a first-order transition to an alternative icosahedra-rich phase. At intermediate bias strengths we find a one-component glassformer.

The suppression of crystallization due to the appearance of structures with fivefold symmetry is widely adopted, but its kinetic and thermodynamic origin remains elusive. Taffs et al. show that fivefold symmetry substantially slows down the nucleation rate but not the crystal growth rate as expected.

Applicability of Dynamic Facilitation Theory to Binary Hard Disk Systems

We numerically investigate the applicability of dynamic facilitation (DF) theory for glass-forming binary hard disk systems where supercompression is controlled by pressure. By using novel efficient algorithms for hard disks, we are able to generate equilibrium supercompressed states in an additive nonequimolar binary mixture, where microcrystallization and size segregation do not emerge at high average packing fractions. Above an onset pressure where collective heterogeneous relaxation sets in, we find that relaxation times are well described by a "parabolic law" with pressure. We identify excitations, or soft spots, that give rise to structural relaxation and find that they are spatially localized, their average concentration decays exponentially with pressure, and their associated energy scale is logarithmic in the excitation size. These observations are consistent with the predictions of DF generalized to systems controlled by pressure rather than temperature.

Population-dynamics method with a multicanonical feedback control

We discuss the Giardinà-Kurchan-Peliti population dynamics method for evaluating large deviations of time-averaged quantities in Markov processes [Phys. Rev. Lett. 96, 120603 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.120603]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dynamical phase transitions. We show how these errors can be mitigated by introducing control forces within the algorithm. These forces are determined by an iteration-and-feedback scheme, inspired by multicanonical methods in equilibrium sampling. We demonstrate substantially improved results in a simple model, and we discuss potential applications to more complex systems.

Nonequilibrium thermodynamic potentials for continuous-time Markov chains

We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.

Phase Transition for Quenched Coupled Replicas in a Plaquette Spin Model of Glasses

We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localized defects and effective kinetic constraints. The thermodynamics of this system is smooth at all temperatures. We show that coupling it to a second system with a fixed (quenched) configuration leads to a phase transition, at finite coupling. The order parameter is the overlap between the copies, and the transition is between phases of low and high overlap. We find critical points whose properties are consistent with random-field Ising universality. We analyze the interfacial free energy cost between the high- and low-overlap states that coexist at (and below) the critical point, and we use this cost as the basis for a finite-size scaling analysis. We discuss these results in the context of mean-field and dynamical facilitation theories of the glass transition.

Using the s ensemble to probe glasses formed by cooling and aging

From length scale distributions characterizing frozen amorphous domains, we relate the s ensemble method with standard cooling and aging protocols for forming glass. We show that in a class of models where space-time scaling is in harmony with that of experiment, the spatial distributions of excitations obtained with the s ensemble are identical to those obtained through cooling or aging, but the computational effort for applying the s ensemble is generally many orders of magnitude smaller than that of straightforward numerical simulation of cooling or aging. We find that in contrast to the equilibrium ergodic state, a nonequilibrium length scale characterizes the anticorrelation between excitations and encodes the preparation history of glass states.

Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics

We consider thermodynamic and dynamic phase transitions in plaquette spin models of glasses. The thermodynamic transitions involve coupled (annealed) replicas of the model. We map these coupled-replica systems to a single replica in a magnetic field, which allows us to analyze the resulting phase transitions in detail. For the triangular plaquette model (TPM), we find for the coupled-replica system a phase transition between high- and low-overlap phases, occurring at a coupling ɛ*(T), which vanishes in the low-temperature limit. Using computational path sampling techniques, we show that a single TPM also displays "space-time" transitions between active and inactive dynamical phases. These first-order dynamical transitions occur at a critical counting field sc(T)≳0 that appears to vanish at zero temperature in a manner reminiscent of the thermodynamic overlap transition. In order to extend the ideas to three dimensions, we introduce the square pyramid model, which also displays both overlap and activity transitions. We discuss a possible common origin of these various phase transitions, based on long-lived (metastable) glassy states.

Dynamic phase coexistence in glass-forming liquids

One of the most controversial hypotheses for explaining the heterogeneous dynamics of glasses postulates the temporary coexistence of two phases characterized by a high and by a low diffusivity. In this scenario, two phases with different diffusivities coexist for a time of the order of the relaxation time and mix afterwards. Unfortunately, it is difficult to measure the single-particle diffusivities to test this hypothesis. Indeed, although the non-Gaussian shape of the van-Hove distribution suggests the transient existence of a diffusivity distribution, it is not possible to infer from this quantity whether two or more dynamical phases coexist. Here we provide the first direct observation of the dynamical coexistence of two phases with different diffusivities, by showing that in the deeply supercooled regime the distribution of the single-particle diffusivities acquires a transient bimodal shape. We relate this distribution to the heterogeneity of the dynamics and to the breakdown of the Stokes-Einstein relation, and we show that the coexistence of two dynamical phases occurs up to a timescale growing faster than the relaxation time on cooling, for some of the considered models. Our work offers a basis for rationalizing the dynamics of supercooled liquids and for relating their structural and dynamical properties.

Weak links between fast mobility and local structure in molecular and atomic liquids

We investigate by molecular-dynamics simulations, the fast mobility-the rattling amplitude of the particles temporarily trapped by the cage of the neighbors-in mildly supercooled states of dense molecular (linear trimers) and atomic (binary mixtures) liquids. The mixture particles interact by the Lennard-Jones potential. The non-bonded particles of the molecular system are coupled by the more general Mie potential with variable repulsive and attractive exponents in a range which is a characteristic of small n-alkanes and n-alcohols. Possible links between the fast mobility and the geometry of the cage (size and shape) are searched. The correlations on a per-particle basis are rather weak. Instead, if one groups either the particles in fast-mobility subsets or the cages in geometric subsets, the increase of the fast mobility with both the size and the asphericity of the cage is revealed. The observed correlations are weak and differ in states with equal relaxation time. Local forces between a tagged particle and the first-neighbour shell do not correlate with the fast mobility in the molecular liquid. It is concluded that the cage geometry alone is unable to provide a microscopic interpretation of the known, universal link between the fast mobility and the slow structural relaxation. We suggest that the particle fast dynamics is affected by regions beyond the first neighbours, thus supporting the presence of collective, extended fast modes.

Brownian dynamics: from glassy to trivial

We endow a system of interacting particles with two distinct, local, Markovian, and reversible microscopic dynamics that both converge to the Boltzmann-Gibbs equilibrium of standard liquids. While the first, standard, one leads to glassy dynamics, we use field-theoretical techniques to show that the latter displays no sign of glassiness. The approximations we use, akin to the mode-coupling approximation, are famous for magnifying glassy aspects of the dynamics, supposedly through the neglect of activated events. Despite this, the modified dynamics seem to stick to standard liquid relaxation. This finding singles out as applying to a realistic system of interacting particles in low dimensions and questions the role of the dynamical rules used to explore a given static free-energy landscape. Moreover, our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.

Flexible confinement leads to multiple relaxation regimes in glassy colloidal liquids

Understanding relaxation of supercooled fluids is a major challenge and confining such systems can lead to bewildering behaviour. Here, we exploit an optically confined colloidal model system in which we use reduced pressure as a control parameter. The dynamics of the system are "Arrhenius" at low and moderate pressure, but at higher pressures relaxation is faster than expected. We associate this faster relaxation with a decrease in density adjacent to the confining boundary due to local ordering in the system enabled by the flexible wall.