Modeling of chemical reaction systems with detailed balance using gradient structures

Abstract

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 the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary $\Gamma$-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

48 pages

References in corpus (3)

• Modeling of chemical reaction systems with detailed balance using gradient structures
• Cross-diffusion systems with excluded volume effects and asymptotic gradient flows
• EDP-convergence for nonlinear fast-slow reaction systems with detailed balance

Cited by in corpus (9)

• Modeling of chemical reaction systems with detailed balance using gradient structures
• Computational Mean-field information dynamics associated with Reaction diffusion equations
• EDP-convergence for nonlinear fast-slow reaction systems with detailed balance
• Cosh gradient systems and tilting
• Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
• Homogenization of Wasserstein gradient flows
• Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions
• A brief overview of existence results and decay time estimates for a mathematical modeling of scintillating crystals
• A gradient flow perspective on McKean-Vlasov equations in econophysics