Convex Analysis of Relaxation Dynamics in Chemical Reaction Networks and Generalized Gradient Flows
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918349654458368 |
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| author | Sugie, Keisuke Loutchko, Dimitri Kobayashi, Tetsuya J. |
| author_facet | Sugie, Keisuke Loutchko, Dimitri Kobayashi, Tetsuya J. |
| contents | We obtain bounds on the Kullback--Leibler divergence to equilibrium for mass-action chemical reaction networks (CRNs) with equilibrium. The associated decay rates are characterized in terms of the singular values of the stoichiometric matrix, convexity parameters, and time-integrated activities via deformed-exponential-type functions. We further extend these bounds within a generalized gradient flow framework. We highlight the biological relevance of this framework: the resulting bounds apply to quasi-steady-state regimes, where long transients and plateau-like behavior are common and functionally important. We illustrate the framework using a catalytic CRN exhibiting plateaus, where the bounds capture slow relaxation induced by local convexity and provide a bound-based approach to quantifying relaxation in CRNs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex Analysis of Relaxation Dynamics in Chemical Reaction Networks and Generalized Gradient Flows Sugie, Keisuke Loutchko, Dimitri Kobayashi, Tetsuya J. Molecular Networks Statistical Mechanics Differential Geometry Optimization and Control Chemical Physics 53B12, 80A30, 90C25, 90C90, 92C45 We obtain bounds on the Kullback--Leibler divergence to equilibrium for mass-action chemical reaction networks (CRNs) with equilibrium. The associated decay rates are characterized in terms of the singular values of the stoichiometric matrix, convexity parameters, and time-integrated activities via deformed-exponential-type functions. We further extend these bounds within a generalized gradient flow framework. We highlight the biological relevance of this framework: the resulting bounds apply to quasi-steady-state regimes, where long transients and plateau-like behavior are common and functionally important. We illustrate the framework using a catalytic CRN exhibiting plateaus, where the bounds capture slow relaxation induced by local convexity and provide a bound-based approach to quantifying relaxation in CRNs. |
| title | Convex Analysis of Relaxation Dynamics in Chemical Reaction Networks and Generalized Gradient Flows |
| topic | Molecular Networks Statistical Mechanics Differential Geometry Optimization and Control Chemical Physics 53B12, 80A30, 90C25, 90C90, 92C45 |
| url | https://arxiv.org/abs/2602.18932 |