Coarse-graining via EDP-convergence for linear fast-slow reaction systems

DOI10.1142/S0218202520500360zbMath1454.60113arXiv1911.06234OpenAlexW3039887769MaRDI QIDQ3386876

Artur Stephan, Alexander Mielke

Publication date: 7 January 2021

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.06234

zbMATH Keywords

coarse grainingenergy-dissipation balanceEDP-convergencereconstruction operatorsentropic gradient structureMarkov process with detailed balance

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Classical flows, reactions, etc. in chemistry (92E20) Markov semigroups and applications to diffusion processes (47D07) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20)

Related Items

Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator, Coarse graining of a Fokker–Planck equation with excluded volume effects preserving the gradient flow structure, Modeling of chemical reaction systems with detailed balance using gradient structures, Evolutionary $\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker--Planck Equations in Multiple Dimensions, Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence, Fast reaction limits via \(\Gamma\)-convergence of the flux rate functional, Cosh gradient systems and tilting, GENERIC framework for reactive fluid flows, Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems, Quantitative Coarse-Graining of Markov Chains, \( \Gamma \)-compactness and \(\Gamma \)-stability of maximal monotone flows, EDP-convergence for a linear reaction-diffusion system with fast reversible reaction, Variational methods for evolution. Abstracts from the workshop held September 6--12, 2020 (hybrid meeting), Jump processes as generalized gradient flows, EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geodesic convexity of the relative entropy in reversible Markov chains
• On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
• On microscopic origins of generalized gradient structures
• Gradient flows of the entropy for finite Markov chains
• Geometric singular perturbation theory for ordinary differential equations
• Instantaneous limits of reversible chemical reactions in presence of macroscopic convection.
• Homogenization of Cahn-Hilliard-type equations via evolutionary \(\Gamma\)-convergence
• Ricci curvature of finite Markov chains via convexity of the entropy
• Separation of time-scales and model reduction for stochastic reaction networks
• An existence result and evolutionary \(\varGamma \)-convergence for perturbed gradient systems
• Fokker-Planck equations for a free energy functional or Markov process on a graph
• Integrals which are convex functionals
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Large deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conduction
• A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
• Evolutionary Γ-convergence of gradient systems modeling slow and fast chemical reactions
• An interesting class of partial differential equations
• The Variational Formulation of the Fokker--Planck Equation
• EDP-convergence for nonlinear fast–slow reaction systems with detailed balance*
• A gradient system with a wiggly energy and relaxed EDP-convergence
• Non-equilibrium Thermodynamical Principles for Chemical Reactions with Mass-Action Kinetics
• On Conjugate Convex Functions
• Probability