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Related papers: Boltzmann equation and hydrodynamic fluctuations

200 papers

Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system. Non-equilibrium…

Statistical Mechanics · Physics 2014-07-17 P. A. Hlushak , M. V. Tokarchuk

In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system…

Analysis of PDEs · Mathematics 2022-05-04 Ricardo J. Alonso , Bertrand Lods , Isabelle Tristani

We consider a linear Boltzmann equation that arises in a model for quantum friction. It describes a particle that is slowed down by the emission of bosons. We study the stochastic process generated by this Boltzmann equation and we show…

Mathematical Physics · Physics 2024-04-25 Roland Bauerschmidt , Wojciech de Roeck , Jürg Fröhlich

The transport coefficients of a dilute classical gas in the presence of a drag force proportional to the velocity of the particle are determined from the Boltzmann equation. The viscous drag force could model the friction of solid particles…

Statistical Mechanics · Physics 2015-06-18 José Carlos Pérez-Fuentes , Vicente Garzó

We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the…

Nuclear Theory · Physics 2018-03-14 Yukinao Akamatsu , Aleksas Mazeliauskas , Derek Teaney

The local-equilibrium approach to transport processes is related to the approach based on time-dependent correlation functions and their associated spectral functions characterizing the equilibrium fluctuations of particle, momentum and…

Statistical Mechanics · Physics 2023-08-16 Joel Mabillard , Pierre Gaspard

The system of hydrodynamic-type equations is derived from Alexeev's generalized Boltzmann kinetic equation by two-side distribution function for a stratified gas in gravity field. It is applied to a problem of ultrasound propagation and…

Fluid Dynamics · Physics 2007-05-23 Sergey B. Leble , Maxim A. Solovchuk

The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the…

Statistical Mechanics · Physics 2014-09-03 Gilberto M. Kremer , Andrés Santos , Vicente Garzó

We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.

Mathematical Physics · Physics 2020-09-03 Giada Basile , Dario Benedetto , Lorenzo Bertini

Green-Kubo and Einstein expressions for the transport coefficients of a fluid in a nonequilibrium steady state can be derived using the Fluctuation Theorem and by assuming the probability distribution of the time-averaged dissipative flux…

Statistical Mechanics · Physics 2009-10-31 Debra J. Searles , Denis J. Evans

We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…

Analysis of PDEs · Mathematics 2022-08-26 Thierry Bodineau , Isabelle Gallagher , Laure Saint-Raymond , Sergio Simonella

An exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors and the theory of slow manifolds, allows us to…

Fluid Dynamics · Physics 2024-11-11 Florian Kogelbauer , Ilya Karlin

We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in underdamped case. The steady state…

Statistical Mechanics · Physics 2009-03-02 Takenobu Nakamura , Akira Yoshimori

Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and…

Statistical Mechanics · Physics 2021-12-16 Hyun-Myung Chun , Qi Gao , Jordan M. Horowitz

Equilibrium properties in statistical physics are obtained by computing averages with respect to Boltzmann-Gibbs measures, sampled in practice using ergodic dynamics such as the Langevin dynamics. Some quantities however cannot be computed…

Numerical Analysis · Mathematics 2023-01-02 Gabriel Stoltz

In molecular dynamics, transport coefficients measure the sensitivity of the invariant probability measure of the stochastic dynamics at hand with respect to some perturbation. They are typically computed using either the linear response of…

Numerical Analysis · Mathematics 2025-02-19 Pierre Monmarché , Renato Spacek , Gabriel Stoltz

We propose a general formalism, within large deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to…

Statistical Mechanics · Physics 2020-12-09 Benjamin Doyon , Jason Myers

We propose a variance reduction method for calculating transport coefficients in molecular dynamics using an importance sampling method via Girsanov's theorem applied to Green--Kubo's formula. We optimize the magnitude of the perturbation…

Numerical Analysis · Mathematics 2025-04-18 Raphaël Gastaldello , Gabriel Stoltz , Urbain Vaes

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse…

Statistical Mechanics · Physics 2009-10-31 Herbert Spohn

We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrodinger…

Mathematical Physics · Physics 2008-11-26 Thomas Curtright , David Fairlie