Related papers: Quantitative Error Estimates for Learning Macrosco…
We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fluctuations in…
Equations of motion for the microscopic number density $\hat{\rho}({\bf x},t)$ and the momentum density $\hat{\bf g}({\bf x},t)$ of a fluid have been obtained in the past from the corresponding Langevin equations representing the dynamics…
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied…
Recently many results namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues…
This work focuses on the quantitative contraction rates for McKean-Vlasov stochastic differential equations (SDEs) with multiplicative noise. Under suitable conditions on the coefficients of the SDE, this paper derives explicit quantitative…
Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an…
Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time…
We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.08 to 12. Hydrodynamic back-flow causes a reduction of the…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that takes into account the response properties that stem from the…
The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant, non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated…
The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters…
$L^2$ norm error estimates of semi- and full discretisations, using bulk--surface finite elements and Runge--Kutta methods, of wave equations with dynamic boundary conditions are studied. The analysis resides on an abstract formulation and…
Collective motion in animal groups emerges from the interplay between individual variability and social coordination, yet connecting these scales quantitatively has remained a major challenge.Using high-resolution trajectories of schooling…
We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the…
The analysis of fluctuation-dissipation relations developed in Giona et al. (2024) for particle hydromechanics is extended to stochastic forcings alternative to Wiener processes, with the aim of addressing the occurrence of Gaussian…
We study parameter estimation for interacting particle systems (IPSs) consisting of $N$ weakly interacting multivariate hypoelliptic SDEs. We propose a locally Gaussian approximation of the transition dynamics, carefully designed to address…
We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…