Related papers: Stochastic theory of nonlinear electrical circuits…
An equilibrium system which is perturbed by an external potential relaxes to a new equilibrium state, a process obeying the fluctuation-dissipation theorem. In contrast, perturbing by nonconservative forces yields a nonequilibrium steady…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…
Near equilibrium, small current fluctuations are described by a Gaussian with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations…
Some limit theorems are proven for the linear oscillator with random coefficients. The asymptotic behaviour of the moments is studied in detail. The technique presented in this paper can be applied to general linear systems with noise and…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
We investigate the dynamical properties of low dimensional systems, driven by external noise sources. Specifically we consider a resistively shunted Josephson junction and a one dimensional quantum liquid in a commensurate lattice…
When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin…
Electronic circuits are built by combining components with known current/voltage characteristics, which are intrinsic to each component and independent of the rest of the circuit. This approach breaks down for nanostructures placed at…
For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the…
We propose a unified framework to study the turbulent transport problem from the perspective of nonequilibrium statistical mechanics. By combining Krarichnan's turbulence thermalization assumption and Ruelle's recent work on nonequilibrium…
Perturbed Einstein's equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out . These perturbations which are stochastic in nature, are of significance for building a…
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random…
We study the statistical properties of currents in two particular systems of capacitively coupled parallel transport channels. In the first system, each transport channel contains a single quantum dot in contact with two electron…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat - the Gallavotti-Cohen Theorem -- relies on the ergodic properties of the system considered. We show that when perturbed by an…
We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of…
The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…