相关论文: Reduced Markovian Descriptions of Brownian Dynamic…

We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original…

In this article we show a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion. Often, Brownian motion is used as an idealized model of a diffusion where approximations such as…

We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…

Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principle model for the impact-velocity dependent restitution coefficient, as it follows…

We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…

Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…

Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…

We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…

We develop a microscopic approach to the kinetic theory of many-particle systems with dissipative and potential interactions in presence of active fluctuations. The approach is based on a generalization of Bogolyubov--Peletminsky reduced…

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…

Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the…

A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in [Colangeli-Duong-Muntean, Journal of Physics A: Mathematical and Theoretical, 2022], based on the Invariant…

The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the…

We develop two-dimensional Brownian dynamics simulations to examine the motion of disks under thermal fluctuations and Hookean forces. Our simulations are designed to be experimental-like, since the experimental conditions define the…

A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order…

Exact and asymptotic formulas relating to dynamical correlations for overdamped Brownian motion are obtained. These formulas include a generalization of the $f$-sum rule from the theory of quantum fluids, a formula relating the static…

The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in…

Brownian motion imposes a hard limit on the overall precision of a nanomechanical measurement. Here, we present a combined experimental and theoretical study of the Brownian dynamics of a quintessential nanomechanical system, a…

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its…

In this paper, using an algorithm based on the retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps,…