First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories

Abstract

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.

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

“…We call these counting observables. An example is the total number of configuration changes in a trajectory, or dynamical activity [11,24,25], sometimes also called "traffic" or "frenesi" [5,26,27]. Here we show that from the bounds to the rate functions of counting observables, via trajectory ensemble equivalence, we can derive the corresponding bounds for arbitrary fluctuations of FPTs.…”

“…While empirical currents are the natural trajectory observables to consider in driven problems [1][2][3][4][5]29,30,33,35,36,40], counting observables such as the dynamical activity are central quantities for systems with complex equilibrium dynamics, such as glass formers [24,25,42,43,46]. (And even for driven systems it is revealing to study the dynamical phase behavior in terms of both empirical currents and activities; see e.g.…”

“…An important observation is that the bounds on fluctuations of a counting observable and its FPTs are controlled by the average dynamical activity, in analogy to the role played by the entropy production in the case of currents [1,13]. We hope these results will add to the growing body of work applying large deviation ideas and methods to the study of dynamics in driven systems [29][30][31][32][33][34][35][36][37][38][39][40][41], glasses [25,[42][43][44][45][46][47], protein folding and signaling networks [48][49][50][51], open quantum systems [52][53][54][55][56][57][58][59][60][61][62][63][64], and many other problems in nonequilibrium [65][66][67][68][69][70][71][72].…”

A minimal model of dynamical phase transition

“…Similar transitions also appear in the long-time fluctuations of time-integrated quantities, such as Lyapunov exponents [16][17][18], dynamical activities [19][20][21][22][23][24][25][26][27][28][29][30], currents [31][32][33][34][35][36][37][38][39], and the entropy production [40][41][42], which now play a central role in studies of nonequilibrium processes. In this case, the large deviation functions are found to be smooth in the long-time limit; singularities start to appear only when a low-noise or a scaling (hydrodynamic, particle or mean-field) limit is taken in addition to the long-time limit [43], leading many to believe and claim that these additional limits are necessary for dynamical phase transitions to appear in Markov processes.…”

Numerical comparison of a constrained path ensemble and a driven quasisteady state

“…Such an ensemble is appealing in that it shares many features of an equilibrium ensemble, and admits elegant techniques for investigation of it properties, both in the case where the constrained dynamical quantity is antisymmetric under time reversal (a flux) [4,5,9], and where it is symmetric (a "dynamical activity") [4,5,[10][11][12][13][14][15][16]. However, it remains unclear whether such ensembles are realized in practise, i.e.…”