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 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 consider ensembles of trajectories associated with large deviations of time-integrated quantities in stochastic models. Motivated by proposals that these ensembles are relevant for physical processes such as shearing and glassy relaxation, we show how they can be generated directly using auxiliary stochastic processes. We illustrate our results using the Glauber-Ising chain, for which biased ensembles of trajectories can exhibit ferromagnetic ordering. We discuss the relation between such biased ensembles and quantum phase transitions.

We describe some of the important physical characteristics of the 'pathways', i.e. dynamical processes, by which molecular, nanoscale and micron-scale self-assembly occurs. We highlight the existence of features of self-assembly pathways that are common to a wide range of physical systems, even though those systems may be different in respect of their microscopic details. We summarize some existing theoretical descriptions of self-assembly pathways, and highlight areas -notably, the description of self-assembly pathways that occur 'far' from equilibrium -that are likely to become increasingly important.

We analyze biased ensembles of trajectories for diffusive systems. In trajectories biased either by the total activity or the total current, we use fluctuating hydrodynamics to show that these systems exhibit phase transitions into "hyperuniform" states, where large-wavelength density fluctuations are strongly suppressed. We illustrate this behavior numerically for a system of hard particles in one dimension and we discuss how it appears in simple exclusion processes. We argue that these diffusive systems generically respond very strongly to any nonzero bias, so that homogeneous states with "normal" fluctuations (finite compressibility) exist only when the bias is very weak.

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.

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.