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Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state…

Statistical Mechanics · Physics 2023-08-09 Timur Aslyamov , Massimiliano Esposito

The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the…

Mathematical Physics · Physics 2007-05-23 Jean-Pierre Eckmann

We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions…

Condensed Matter · Physics 2009-10-28 E. L. Grossman , T. Zhou , E. Ben-Naim

We study the solution of the two-temperatures Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of…

Mathematical Physics · Physics 2024-03-08 Diego Alberici , Nicolas Macris , Emanuele Mingione

We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host-medium with a fixed distribution. This is achieved by controlling the Lp-norms, the moments and the…

Analysis of PDEs · Mathematics 2009-11-13 Marzia Bisi , Jose A. Carrillo , Bertrand Lods

In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed…

Probability · Mathematics 2021-11-02 Arnulf Jentzen , Felix Lindner , Primož Pušnik

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange…

Statistical Mechanics · Physics 2010-11-10 S. Lepri , C. Mejia-Monasterio , A. Politi

Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in…

Statistical Mechanics · Physics 2022-07-05 Boris Rotstein , Eric Akkermans

We consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity ($L^p$-regularity in the velocity-variable and Sobolev regularity in the…

Probability · Mathematics 2017-05-16 Ennio Fedrizzi , Franco Flandoli , Enrico Priola , Julien Vovelle

Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…

Statistical Mechanics · Physics 2009-10-31 K. Ø. Rasmussen , T. Cretegny , P. G. Kevrekidis , N. Grønbech-Jensen

By using the analytic tools of Dirichlet forms, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along a fractal (which can be considered as a simplified rough porous…

Classical Analysis and ODEs · Mathematics 2024-10-10 Xuan Liu , Zhongmin Qian

We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in ${\mathbb R}^n_+ \times (0,T)$. We obtain new estimates of solutions including pressure in terms of mixed anisotropic…

Analysis of PDEs · Mathematics 2013-08-08 Tongkeun Chang , Kyungkeun Kang

We consider two methods to establish log-Sobolev inequalities for the invariant measure of a diffusion process when its density is not explicit and the curvature is not positive everywhere. In the first approach, based on the Holley-Stroock…

Probability · Mathematics 2025-03-25 Pierre Monmarché , Songbo Wang

Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the positivity of temperature. So far, no global existence results…

Analysis of PDEs · Mathematics 2023-12-20 Tomasz Cieślak , Boris Muha , Srđan Trifunović

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

This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…

Fluid Dynamics · Physics 2024-11-08 Rômulo Damasclin Chaves dos Santos

In this paper we prove the global existence and uniqueness of the low regularity solutions to the Cauchy problem of quasi-linear wave equations with radial symmetric initial data in three space dimensions. The results are based on the…

Analysis of PDEs · Mathematics 2007-05-23 Yi Zhou , Zhen Lei

We prove the existence of density for the solution to the multiplicative semilinear stochastic heat equation on an unbounded spatial domain, with drift term satisfying a half-Lipschitz type condition. The methodology is based on a careful…

Probability · Mathematics 2023-02-22 Michael Salins , Samy Tindel

This paper investigates a damped stochastic wave equation driven by a non-Gaussian Levy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition…

Probability · Mathematics 2009-05-08 Lijun Bo , Kehua Shi , Yongjin Wang

Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances…

Mathematical Physics · Physics 2012-04-27 A. C. D. van Enter