---
_id: '8758'
abstract:
- lang: eng
  text: 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.
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).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jan
  full_name: Maas, Jan
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
- first_name: Alexander
  full_name: Mielke, Alexander
  last_name: Mielke
citation:
  ama: Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance
    using gradient structures. <i>Journal of Statistical Physics</i>. 2020;181(6):2257-2303.
    doi:<a href="https://doi.org/10.1007/s10955-020-02663-4">10.1007/s10955-020-02663-4</a>
  apa: Maas, J., &#38; Mielke, A. (2020). Modeling of chemical reaction systems with
    detailed balance using gradient structures. <i>Journal of Statistical Physics</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s10955-020-02663-4">https://doi.org/10.1007/s10955-020-02663-4</a>
  chicago: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems
    with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>.
    Springer Nature, 2020. <a href="https://doi.org/10.1007/s10955-020-02663-4">https://doi.org/10.1007/s10955-020-02663-4</a>.
  ieee: J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed
    balance using gradient structures,” <i>Journal of Statistical Physics</i>, vol.
    181, no. 6. Springer Nature, pp. 2257–2303, 2020.
  ista: Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed
    balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303.
  mla: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with
    Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>,
    vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:<a href="https://doi.org/10.1007/s10955-020-02663-4">10.1007/s10955-020-02663-4</a>.
  short: J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.
corr_author: '1'
date_created: 2020-11-15T23:01:18Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2025-06-12T07:01:39Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s10955-020-02663-4
ec_funded: 1
external_id:
  arxiv:
  - '2004.02831'
  isi:
  - '000587107200002'
  pmid:
  - '33268907'
file:
- access_level: open_access
  checksum: bc2b63a90197b97cbc73eccada4639f5
  content_type: application/pdf
  creator: dernst
  date_created: 2021-02-04T10:29:11Z
  date_updated: 2021-02-04T10:29:11Z
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file_date_updated: 2021-02-04T10:29:11Z
has_accepted_license: '1'
intvolume: '       181'
isi: 1
issue: '6'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 2257-2303
pmid: 1
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: F06504
  name: Taming Complexity in Partial Differential Systems
publication: Journal of Statistical Physics
publication_identifier:
  eissn:
  - 1572-9613
  issn:
  - 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modeling of chemical reaction systems with detailed balance using gradient
  structures
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 181
year: '2020'
...