Related papers: On the ergodicity breaking in well-behaved General…
For discrete-time Markov chains on general state spaces, we establish criteria for non-ergodicity and non-strong ergodicity, and derive sufficient conditions for non-geometric ergodicity via the theory of minimal nonnegative solutions. Our…
The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants.…
Distributed asynchronous SGD has become widely used for deep learning in large-scale systems, but remains notorious for its instability when increasing the number of workers. In this work, we study the dynamics of distributed asynchronous…
Various qualitative properties of solutions to the generalized Langevin equation (GLE) in a periodic or a confining potential are studied in this paper. We consider a class of quasi-Markovian GLEs, similar to the model that was introduced…
Coarse-grained (CG) models are simplified representations of soft matter systems that are commonly employed to overcome size and time limitations in computational studies. Many approaches have been developed to construct and parametrise…
The emergence of self-sustained clusters and their role in ergodicity breaking is investigated in fully connected Ising and Sherrington-Kirkpatick (SK) models. The analysis reveals a clustering behavior at various parameter regimes, as well…
A reaction network consists of a finite number of species, which interact through predefined reaction channels. Traditionally such networks were modeled deterministically, but it is now well-established that when reactant copy numbers are…
In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…
In this paper, we study the diffusive limit of solutions to the generalized Langevin equation (GLE) in a periodic potential. Under the assumption of quasi-Markovianity, we obtain sharp longtime equilibration estimates for the GLE using…
Most natural thermodynamic systems operate far from equilibrium, developing persistent currents and organizing into non-equilibrium stationary states (NESSs). Yet, the principles by which such systems self-organize, breaking equilibrium…
This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…
A generic closed quantum many-body system will inevitably tend to thermalization, whose local information encoded in the initial state eventually scrambles into the full space, known as quantum ergodicity. A paradigmatic exception in closed…
These notes present an alternative approach to the asymptotic stability of stochastic partial differential equations driven by multiplicative noise, applicable to a wide range of dissipative systems. The method builds on general criteria…
The generalized elastic model encompasses several physical systems such as polymers, membranes, single file systems, fluctuating surfaces and rough interfaces. We consider the case of an applied localized potential, namely an external force…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
Recently, a couple of investigations related to symmetry breaking phenomena, 'spontaneous stochasticity' and 'ergodicity breaking' have led to significant impacts in a variety of fields related to the stochastic processes such as economics…
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential…
The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…
Complex dissipative systems appear across science and engineering, from polymers and active matter to learning algorithms. These systems operate far from equilibrium, where energy dissipation and time irreversibility govern their behavior…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…