Related papers: Fluctuation-dissipation relations for stochastic g…
We derive the stationary fluctuations for the Facilitated Exclusion Process (FEP) in one dimension in the symmetric, weakly asymmetric and asymmetric cases. Our proof relies on the mapping between the FEP and the zero-range process, and…
The fluctuation-dissipation relation, a central result in non-equilibrium statistical physics, relates equilibrium fluctuations in a system to its linear response to external forces. Here we provide a direct experimental verification of…
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
Stochastic gradient descent is a classic algorithm that has gained great popularity especially in the last decades as the most common approach for training models in machine learning. While the algorithm has been well-studied when…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
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…
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of reaction…
Recently Mayer et al. [Phys. Rev. E {\bf 68}, 016116 (2003)] proposed a new way to compute numerically the fluctuation-dissipation ratios in nonequilibrium critical systems. Using well-known facts of nonequilibrium critical dynamics I show…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic…
We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By…
In this note, we present a simple derivation, from time-reversal symmetry, of fluctuation relations for steady-state large deviation functions in non-equilibrium quantum systems. We further show that a condition of pure transmission implies…
We study a class of non-equilibrium lattice models describing local redistributions of a globally conserved quantity, which is interpreted as an energy. A particular subclass can be solved exactly, allowing to define a statistical…
In linear transport, the fluctuation-dissipation theorem relates equilibrium current correlations to the linear conductance coefficient. For nonlinear transport, there exist fluctuation relations that rely on Onsager's principle of…
We investigated the validity of fluctuation-dissipation relations in the nonequilibrium stationary state of fluidized granular media under gravity by two independent approaches, based on theory and numerical simulations. A phenomenological…
Currents of particles or energy in driven nonequilibrium steady states are known to satisfy certain symmetries, referred to as fluctuation relations, determining the ratio of the probabilities of positive fluctuations to negative ones. A…
For systems close to equilibrium, the relaxation properties of measurable physical quantities are described by the linear response theory and the fluctuation-dissipation theorem (FDT). Accordingly, the response or the generalized…
The article provides a unitary and complete solution to the fluctuation-dissipation relations for particle hydromechanics in a generic fluid, accounting for the hydrodynamic fluid-particle interactions (including arbitrary memory kernels in…
In this perspective we consider how modern statistical mechanics and response theory can be applied to understand the response of polar molecules to an applied electric field and the fluctuations in these systems. Results that are…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…