Related papers: On time's arrow in Ehrenfest models with reversibl…
We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by…
We study dynamical fluctuations in the macroscopic paths around the most probable path of the Kac ring model, which is a simple deterministic and reversible dynamical system exhibiting the macroscopic irreversible relaxation. We derive the…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse…
The evolution of physical systems are often modeled by simple Markovian processes. When settled into stationary states, the probability distributions of such systems are time independent, by definition. However, they do not necessarily fall…
Emergence of one-time-direction macroscopic evolution of a classical system of two mixed gases having different temperatures is derived and explained. The analysis performed at the microscopic level, where the time-symmetric laws of…
One key challenge in the study of nonadiabatic dynamics in open quantum systems is to balance computational efficiency and accuracy. Although Ehrenfest dynamics (ED) is computationally efficient and well-suited for large complex systems, ED…
We study the semiclassical Ehrenfest trajectories in open quantum systems. We first derive in explicit form the Fokker-Planck equation that governs the time evolution of the mixing measure for a Gaussian mixture. Then, we embed the…
The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
The Ehrenfest dynamics, representing a quantum-classical mean-field type coupling, is a widely used approximation in quantum molecular dynamics. In this paper, we propose a time-splitting method for an Ehrenfest dynamics, in the form of a…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
Systems with long-range interactions often relax towards statistical equilibrium over timescales that diverge with $N$, the number of particles. A recent work [S. Gupta and D. Mukamel, J. Stat. Mech.: Theory Exp. P03015 (2011)] analyzed a…
A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally…
Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed…
The spread of the time arrows from the environment to an observed subsystem is followed within a harmonic model. A similarity is pointed out between irreversibility and a phase with spontaneously broken symmetry. The causal structure of…
We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd \times E where E is a finite set. The continuous component evolves according to a smooth vector field that…
In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in determin-istic dynamical systems. We demonstrate that the genealogical particle analysis algorithms can…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
We consider a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious epidemic model in which the transmission intensity function is time-dependent. Such a model is well suited to…