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A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…

Mathematical Physics · Physics 2011-10-14 Miguel Escobedo , Federica Pezzotti

Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…

Dynamical Systems · Mathematics 2018-11-14 Jacek Banasiak , Luke O. Joel , Sergey Shindin

Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the…

Statistical Mechanics · Physics 2018-10-01 A. Bhattacharyay

We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the…

Analysis of PDEs · Mathematics 2009-02-20 Bertrand Lods , Clément Mouhot , Giuseppe Toscani

The paper considers the convergence to equilibrium for measure solutions of the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. We prove the exponential sharp rate of strong convergence to equilibrium for…

Analysis of PDEs · Mathematics 2015-01-27 Lu Xuguang , Clément Mouhot

The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…

Statistical Mechanics · Physics 2020-08-05 Xhek Turkeshi , Paola Ruggiero , Vincenzo Alba , Pasquale Calabrese

We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…

Analysis of PDEs · Mathematics 2012-05-22 Ondrej Budáč , Michael Herrmann , Barbara Niethammer , Andrej Spielmann

A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…

Statistical Mechanics · Physics 2021-04-29 Yogyata Pathania , Dipanjan Chakraborty , Felix Höfling

The exponential decay of the relative entropy associated to a fully discrete porous-medium equation in one space dimension is shown by means of a discrete Bakry-Emery approach. The first ingredient of the proof is an abstract discrete…

Analysis of PDEs · Mathematics 2017-02-14 Ansgar Jüngel , Stefan Schuchnigg

The dynamics of a coagulation-fragmentation equation with multiplicative coagulation kernel and critical singular fragmentation is studied. In contrast to the coagulation equation, it is proved that fragmentation prevents the occurrence of…

Analysis of PDEs · Mathematics 2014-07-08 Philippe Laurencot , Henry Van Roessel

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit…

Dynamical Systems · Mathematics 2017-09-01 Sébastien Gouëzel , Ian Melbourne

Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed…

Statistical Mechanics · Physics 2013-09-03 Akihisa Ichiki , Masayuki Ohzeki

The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo-Martin-Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of open quantum…

Quantum Physics · Physics 2007-05-23 Luigi Accardi , Kentaro Imafuku

We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…

Analysis of PDEs · Mathematics 2020-10-02 Hiroyoshi Mitake , Hung V. Tran , Truong-Son Van

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

Probability · Mathematics 2007-05-23 Clive G. Wells

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…

Analysis of PDEs · Mathematics 2018-10-16 Jan Haskovec , Sabine Hittmeir , Peter Markowich , Alexander Mielke

The quasi--equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions…

Statistical Mechanics · Physics 2009-11-07 Patrick Ilg , Iliya V. Karlin , Hans Christian Öttinger

Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…

Probability · Mathematics 2016-11-22 Nathanael Hoze , David Holcman

We consider discretizations of the Einstein action of general relativity such that the resulting discrete equations of motion form a consistent constrained system. Upon ``spin foam'' quantization of the system, consistency allows a natural…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Rodolfo Gambini , Jorge Pullin

We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schr\"odinger equation with diffusive forcing.…

Mathematical Physics · Physics 2017-12-29 Eric A. Carlen , Jürg Fröhlich , Joel Lebowitz , Wei-Min Wang