Modeling of chemical reaction systems with detailed balance using gradient structures

J. Maas, A. Mielke, Journal of Statistical Physics (2020).


Journal Article | Epub ahead of print | English

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Author
Maas, JanIST Austria ; Mielke, Alexander
Department
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 Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.
Publishing Year
Date Published
2020-11-06
Journal Title
Journal of Statistical Physics
Acknowledgement
The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex Systems (Project No. 235221301), through the Subproject C05 Effective models for materials and interfaces with multiple scales. J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117), and by the Austrian Science Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson, and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding provided by Austrian Science Fund (FWF).
ISSN
eISSN
IST-REx-ID

Cite this

Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 2020. doi:10.1007/s10955-020-02663-4
Maas, J., & Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. https://doi.org/10.1007/s10955-020-02663-4
Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics, 2020. https://doi.org/10.1007/s10955-020-02663-4.
J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” Journal of Statistical Physics, 2020.
Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics.
Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics, Springer Nature, 2020, doi:10.1007/s10955-020-02663-4.
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