bibkey: maasmielke2020reaction authors: Jan Maas and Alexander Mielke year: 2020 title: Modeling of chemical reaction systems with detailed balance using gradient structures doi: null url: https://arxiv.org/pdf/2004.02831v1 claim: “A mass-action reaction-rate equation with positive detailed-balanced reference concentration has a relative-entropy gradient structure with logarithmic-mean mobility.” strata_touched: [] license: citation-only triage: anchor
Reaction entropy and the level of the state
The cited version is arXiv:2004.02831v1. Section 1 and Section 2.1 distinguish concentration-valued reaction-rate equations from the chemical master equation on particle counts. Section 2.3, printed pp. 8–9, equations (2.9)–(2.12) and Theorem 2.2, states the entropy gradient structure under detailed balance at a positive reference concentration. Its logarithmic mean is , continued as at . The authors attribute antecedents of this gradient structure to Yong and Mielke; no historical priority beyond the cited statement is asserted.
The consumer is Static §24, Assumption 24.3 and Theorem 24.4. The reaction supplies a particular normalized vector field. The theorem separately constructs its law-dependent single-state directed-cycle realization. Reaction detailed balance and edge detailed balance of that realization have different conditions; the reaction theorem does not assert the latter. The five-state embedding, bounded polynomial rates and nonuniform Gibbs example are the consumer’s application, not statements quoted from this paper.