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This paper concerns with the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain…
The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed…
We consider a class of noisy, one-dimensional quantum cellular automata that allow one to shift from unitary dynamics to completely positive maps, and investigate the notion of reversibility in such a setting. To this aim, we associate an…
We discuss the influence of white noise on a generic dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous…
We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…
For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these…
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this…
We present a chemical reaction network that is unstable under deterministic mass action kinetics, exhibiting finite-time blow-up of trajectories in the interior of the state space, but whose stochastic counterpart is positive recurrent.…
In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non Gaussian noise. In agreement with the theoretical predictions our main findings are:…
The literature on dynamical systems has, for the most part, considered self-oscillators (i.e., systems capable of generating and maintaining a periodic motion at the expense of an external energy source with no corresponding periodicity)…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…