We show that the dynamics of kinetically constrained models of glass formers takes place at a firstorder coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states. An increasingly accepted view is that the phenomenology associated with the glass transition [1] requires a purely dynamic analysis, and does not arise from an underlying static transition (see however [2]). Indeed, it has been suggested that the glass transition manifests a firstorder phase transition in space and time between active and inactive phases [3]. Here we apply Ruelle's thermodynamic formalism [4,5] to show that this suggestion is indeed correct, for a specific class of stochastic models. The existence of active and inactive regions of spacetime, separated by sharp interfaces, is dynamic heterogeneity, a central feature of glass forming systems [6]. This phenomenon, in which the dynamics becomes increasingly spatially correlated at low temperatures, arises naturally [7] in models based on the idea of dynamic facilitation, such as spin-facilitated models [8,9], constrained lattice gases [10,11] and other kinetically constrained models (KCMs) [12]. Fig. 1 illustrates the discontinuities in space-time order parameters at the dynamical transition in one such model, together with the singularity in a space-time free energy, as a function of a control parameter to be discussed shortly.The thermodynamic formalism of Ruelle and coworkers was developed in the context of deterministic dynamical systems [4]. While traditional thermodynamics is used to study fluctuations associated with configurations of a system, Ruelle's formalism yields information about its trajectories (or histories). The formalism relies on the construction of a dynamical partition function, analogous to the canonical partition function of thermodynamics. The energy of the system is replaced by the dynamical action (the negative of the logarithm of the probability of a given history); the entropy of the system by the Kolmogorov-Sinai entropy [13], and the temperature by an intrinsic field conjugate to the action. This formalism has been exploited recently to describe the chaotic properties of continuous-time Markov processes [5].In this work, we define the dynamical partition sum [4, where the sum is over histories from time 0 to time t; the probability of a history is Prob(history); andK(history) is the number of configuration changes in that history. K(history) is a direct measure of the activity in a history: an active trajectory has many changes of configur...

The glass transition is the freezing of a liquid into a solid state without evident structural order. Although glassy materials are well characterized experimentally, the existence of a phase transition into the glass state remains controversial. Here, we present numerical evidence for the existence of a novel first-order dynamical phase transition in atomistic models of structural glass formers. In contrast to equilibrium phase transitions, which occur in configuration space, this transition occurs in trajectory space, and it is controlled by variables that drive the system out of equilibrium. Coexistence is established between an ergodic phase with finite relaxation time and a nonergodic phase of immobile molecular configurations. Thus, we connect the glass transition to a true phase transition, offering the possibility of a unified picture of glassy phenomena.

We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one dimensional (d = 1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of d+1 dimensional dense mixtures of polydisperse non-interpenetrating domains. The domains coincide with arrested regions in trajectory space.PACS numbers: 64.70. Pf, 75.10.Hk, 05.70.Ln A glass forming system, like a supercooled liquid, exhibits a precipitous onset of slowness. As temperature is decreased in these systems, typically in a range of a few decades, relaxation times and viscosities increase by several orders of magnitude, eventually surpassing experimentally accessible times. For practical purposes, these systems effectively freeze at the glass transition temperature T g . For reviews see [1]. Interestingly, this dynamical arrest carries no evident static structural signature of growing length scales. Rather, experiments and simulations show that supercooled liquids are dynamically heterogeneous [2,3]. Molecules in one region of the liquid translate or rotate several orders of magnitude faster or slower than those in a neighboring region. The spatial extent of these dynamical heterogeneities is mesoscopic, and the time scale of the slowest domains increases with decreasing temperature at least as fast as the relaxation time of the system. Such structural behavior seems beyond description with homogeneous methods like mode coupling [4] and mean field theories [5], and it is widely neglected in analytical treatments (see, however, [6-8]). Nevertheless, we show here that for a broadly applicable mechanism of dynamical arrest, these heterogeneities are intrinsic to the nature of glass forming systems.Our central result is that dynamical heterogeneities are a manifestation of the existence of nontrivial structure in the trajectories of glassy systems. This structure associated with dynamics is independent of any specific static properties. Instead, the nontrivial dynamical structure is a consequence of local dynamical rules that significantly restrict the size of accessible trajectory space. For example, consider a highly compressed (or supercooled) glass former. Atoms in most regions of space are jammed, making mobility possible in only a relatively low fraction of spatial regions. These rare regions are those that are already unjammed, or those that may be close in space to an unjammed region. In the evolution of such a system, one therefore expects a clustering of mobile regions and thus a mesoscopic demixing of mobile and static regions. Macroscopic demixing is not expected because dynamics should conserve a canonical distribution. This picture of the origin of dynamic heterogeneity is in accord with the idea that glassiness is no...

We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit a first-order dynamical transition between active and inactive dynamical phases. We argue that the dynamical heterogeneities displayed by these systems are a manifestation of dynamical first-order phase coexistence. In particular, we calculate dynamical large deviation functions, both analytically and numerically, for the Fredrickson-Andersen model, the East model, and constrained lattice gas models. We also show how large deviation functions can be obtained from a Landau-like theory for dynamical fluctuations. We discuss possibilities for similar dynamical phase-coexistence behaviour in other systems with heterogeneous dynamics.

We review a theoretical perspective of the dynamics of glass-forming liquids and the glass transition, a perspective developed during this past decade based on the structure of trajectory space. This structure emerges from spatial correlations of dynamics that appear in disordered systems as they approach nonergodic or jammed states. It is characterized in terms of dynamical heterogeneity, facilitation, and excitation lines. These features are associated with a newly discovered class of nonequilibrium phase transitions. Equilibrium properties have little, if anything, to do with it. The broken symmetries of these transitions are obscure or absent in spatial structures, but they are vivid in space-time (i.e., trajectory space). In our view, the glass transition is an example of this class of transitions. The basic ideas and principles we review were originally developed through the analysis of idealized and abstract models. Nevertheless, the central ideas are easily illustrated with reference to molecular dynamics of more realistic atomistic models, and we use that illustrative approach here.

We apply the large-deviation method to study trajectories in dissipative quantum systems. We show that in the long time limit the statistics of quantum jumps can be understood from thermodynamic arguments in terms of dynamical phases and transitions between them in trajectory space. We illustrate our approach with three simple examples: a driven 2-level system where we find a particular scale invariance point in the ensemble of trajectories of emitted photons; a blinking 3-level system, where we argue that intermittency in the photon count is related to a crossover between distinct dynamical phases; and a micromaser, where we find an actual first-order phase transition in the ensemble of trajectories.

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, D ∼ τ −1 , where D is the self diffusion constant and τ is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality d, going as D ∼ τ −2/3 for d = 1, and as D ∼ τ −0.95 for d = 3. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for d = 1, D ∼ τ −0.73 . This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.

We provide here a brief perspective on the glass transition field. It is an assessment, written from the point of view of theory, of where the field is and where it seems to be heading. We first give an overview of the main phenomenological characteristics, or "stylised facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner. We describe recent developments, with a particular focus on real space properties, including dynamical heterogeneity and facilitation, the search for underlying spatial or structural correlations, and the relation between the thermal glass transition and athermal jamming. We then discuss briefly how competing theories of the glass transition have adapted and evolved to account for such real space issues. We consider in detail two conceptual and methodological approaches put forward recently, that aim to access the fundamental critical phenomenon underlying the glass transition, be it thermodynamic or dynamic in origin, by means of biasing of ensembles, of configurations in the thermodynamic case, or of trajectories in the dynamic case. We end with a short outlook.