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We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
In stochastic modeling, the excess entropy -- the mutual information shared between a process's past and future -- represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated…
Threshold and infrared divergences are studied as possible mechanisms of particle production and compared to the usual decay process in a model quantum field theory from which generalizations are obtained. A spectral representation of the…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
Under an oscillating mechanical drive, an amorphous material progressively forgets its initial configuration and might eventually converge to a limit cycle. Beyond quasistatic drivings, how structurally disordered systems lose or record…
We consider a system of non-interacting Brownian particles on a line with a step-like initial condition, and we investigate the behavior of the local time at the origin at large times. We compute the mean and the variance of the local time,…
In this article we want to demonstrate that the time-scale constraints for a thermodynamic system imply the new concept of {\it equipartition of energy bound} (EEB) or, more generally, a thermodynamical bound for the {\it partition} of…
Out-of-equilibrium disordered systems may form memories of external driving in a remarkable fashion. The system "remembers" multiple values from a series of training inputs yet "forgets" nearly all of them at long times despite the inputs…
One of the fundamental arguments in quantum information theory is the uncertainty principle. In accordance with this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
The features for the unsteady process of thermal equilibration ("the fast motions") in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements…
We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the "exponential decay" of the memory…
The Brownian motion of a particle immersed in a medium of charged particles is considered when the system is placed in magnetic or electric fields. Coming from the Zwanzig-Caldeira-Legget particle-bath model, we modify it so that not only…
We study a temporally third order (Moore-Gibson-Thompson) equation with a memory term. Previously it is known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known…
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this study, we investigate the heat dissipation associated with finite-time information erasure…
Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with…
We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model…