Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems

Abstract

In a recent article [M. Merolle et al., Proc. Natl. Acad. Sci. USA 102, 10837 (2005)] it was argued that dynamic heterogeneity in $d$-dimensional glass formers is a manifestation of an order-disorder phenomenon in the $d+1$ dimensions of spacetime. By considering a dynamical analogue of the free energy, evidence was found for phase coexistence between active and inactive regions of spacetime, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic spacetime observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a non-equilibrium theory in the directed percolation universality class.

12 pages, 11 figures, final version with minor changes

References in corpus (6)

• Glassy dynamics of kinetically constrained models
• Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids
• Time Resolved Correlation measurements of temporally heterogeneous dynamics
• Dynamical Exchanges in Facilitated Models of Supercooled liquids
• Mappings between reaction-diffusion and kinetically constrained systems: A+A <-> A and the FA model have upper critical dimension d_c=2
• Subdiffusion and dynamical heterogeneities in a lattice glass model

Cited by in corpus (6)

• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Non-equilibrium dynamics of spin facilitated glass models
• Aging in One-Dimensional Coagulation-Diffusion Processes and the Fredrickson-Andersen Model
• Slow relaxation, dynamic transitions and extreme value statistics in disordered systems
• Dynamic propensity in a kinetically constrained lattice gas