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The convergence to equilibrium of renormalized solutions to reaction-cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from…

Analysis of PDEs · Mathematics 2018-08-20 Esther S. Daus , Bao Quoc Tang

By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…

Machine Learning · Computer Science 2023-04-17 Hengtong Zhang , Tingyang Xu

In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…

Analysis of PDEs · Mathematics 2016-12-19 Klemens Fellner , Wolfgang Prager , Bao Q. Tang

A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…

Statistical Mechanics · Physics 2015-06-25 M. Nitti , A. Torcini , S. Ruffo

Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…

Statistical Mechanics · Physics 2015-07-20 Jorge Fernandez-de-Cossio , Jorge Fernandez-de-Cossio Diaz

The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be…

Biological Physics · Physics 2009-11-11 Holger Merlitz , Konstantin V. Klenin , Chen-Xu Wu , Jörg Langowski

We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…

Analysis of PDEs · Mathematics 2020-12-02 Jan Maas , Alexander Mielke

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Analysis of PDEs · Mathematics 2024-12-17 Laurent Desvillettes , Kim Dang Phung , Bao Quoc Tang

Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…

Pattern Formation and Solitons · Physics 2021-05-14 Andrew L. Krause , Václav Klika , Philip K. Maini , Denis Headon , Eamonn A. Gaffney

Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…

Fluid Dynamics · Physics 2019-04-23 T. -W. Lee

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…

Biological Physics · Physics 2024-07-22 Mohamed Swailem , Uwe C. Täuber

The maximum entropy method has recently been successfully introduced to a variety of natural language applications. In each of these applications, however, the power of the maximum entropy method is achieved at the cost of a considerable…

cmp-lg · Computer Science 2008-02-03 John D. Lafferty , Bernhard Suhm

Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…

Statistical Mechanics · Physics 2026-03-13 Eric R. Heller , David T. Limmer

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

Machine Learning · Computer Science 2025-08-14 Denis Blessing , Julius Berner , Lorenz Richter , Gerhard Neumann

An active area of research interest is the inference of ecological models of complex microbial communities. Inferring such ecological models entails understanding the interactions between microbes and how they affect each other's growth.…

Applications · Statistics 2022-10-19 William Krinsman

Significant progress has been made on the model development for simulating turbulent reacting flows. As a consequence, we are currently in a position where key-physical aspects of fairly complex combustion processes are well understood at a…

Fluid Dynamics · Physics 2020-12-17 Matthias Ihme

Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…

patt-sol · Physics 2007-05-23 Silvina Ponce Dawson , Maria Veronica D'Angelo , John E. Pearson

We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…

Statistical Mechanics · Physics 2009-11-07 Vahid Karimipour

We present a series of closed-form maximum entropy upper bounds for the differential entropy of a continuous univariate random variable and study the properties of that series. We then show how to use those generic bounds for upper bounding…

Information Theory · Computer Science 2026-01-06 Frank Nielsen , Richard Nock

This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…

Chaotic Dynamics · Physics 2009-11-07 J. R. Dorfman , P. Gaspard , T. Gilbert