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Slow dynamics in disordered materials prohibits direct simulation of their rich nonequilibrium behavior at large scales. "Patchwork dynamics" is introduced to mimic relaxation over a very broad range of time scales by equilibrating or…

This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…

Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…

Elastic models of the glass transition relate the relaxation dynamics and the elastic properties of structural glasses. They are based on the assumption that the relaxation dynamics occurs through activated events in the energy landscape…

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi…

We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical…

In the study of the thermalization of closed quantum systems, the role of kinetic constraints on the temporal dynamics and the eventual thermalization is attracting significant interest. Kinetic constraints typically lead to long-lived…

Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…

Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…

We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the…

We define restricted ensembles, called pico-canonical ensembles, for a statistical-mechanical description of the metastable and glassy phases. In this approach, time-evolution is Markovian, with temperature dependent rates. Below a…

We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce…

We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…

The definition of metastable states is an ubiquitous task in the design and analysis of molecular simulations, and is a crucial input in a variety of acceleration methods for the sampling of long configurational trajectories. Although…

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…

Two-dimensional decaying turbulent flow is known to approach apparently stable states after a long time evolution. A few theories and models have been so far proposed to account for this relaxation. In this paper, we compare results of…

We consider large deviations of the dynamical activity in the East model. We bias this system to larger than average activity and investigate the structure that emerges. To best characterise this structure, we exploit the fact that there…

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a non-equilibrium phase transition or a smooth but sharp…

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…

We investigate mixed eigenstates in systems with sharply-divided phase space, using different piecewise-linear maps whose regular-chaotic boundaries are formed by marginally unstable periodic orbits (MUPOs) or by quasi-periodic orbits. With…