WIAS Preprint No. 2712, (2020)

Modeling of chemical reaction systems with detailed balance using gradient structures


  • Maas, Jan
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 34E13 35Q84 37L45 60J28


  • Reaction-rate equation, chemical master equation, Fokker-Planck equation, chemical Langevin dynamics, detailed-balance condition, relative entropy, dissipation potentials, gradient structures, many-particle limit




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 Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

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