{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:02:53Z","timestamp":1785423773579,"version":"3.56.0"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T00:00:00Z","timestamp":1784505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12205135"],"award-info":[{"award-number":["12205135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["12205135"],"award-info":[{"award-number":["12205135"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005270","name":"Natural Science Foundation of Fujian Province of China","doi-asserted-by":"publisher","award":["2024J01212"],"award-info":[{"award-number":["2024J01212"]}],"id":[{"id":"10.13039\/501100005270","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems","award":["2024B1212010004"],"award-info":[{"award-number":["2024B1212010004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We present a systematic derivation of asymptotic expansions of nonequilibrium thermodynamics for chemical reaction networks (CRNs) based on singular perturbation theory. For a general reversible CRN with fast\u2013slow kinetics, we obtain the first and second laws of thermodynamics for the asymptotic expansion model. We derive composite expansions of the enthalpy, entropy, entropy production rate, and relative entropy. The slow-varying outer parts of these thermodynamic quantities capture the long-time trend, while the fast-varying corrected inner parts decay to zero as the fast time variable tends to infinity. The convergence order of these quantities is determined by the local Lipschitz properties of the respective functions. The enthalpy retains the same convergence order as the kinetic variables, whereas the entropy, relative entropy, and entropy production rate involve logarithmic terms that cause their gradients to diverge when some concentrations approach zero, reducing their theoretical convergence order by one. The general theory is validated on the reversible Michaelis\u2013Menten reaction, for which both leading-order and first-order matched asymptotic expansions are obtained analytically. Numerical simulations confirm the uniform accuracy of the composite thermodynamic approximations and further reveal that the entropy production rate converges with a higher order than theoretically predicted. The results demonstrate that the composite expansion provides a rigorous and physically consistent tool for analyzing energy and entropy balances in multiscale CRNs.<\/jats:p>","DOI":"10.3390\/e28070825","type":"journal-article","created":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T13:18:31Z","timestamp":1784553511000},"page":"825","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Thermodynamics for Chemical Reaction Networks with Fast-Slow Kinetics"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6843-8987","authenticated-orcid":false,"given":"Liangrong","family":"Peng","sequence":"first","affiliation":[{"name":"School of Computer and Big Data, Minjiang University, Fuzhou 350108, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4040-4005","authenticated-orcid":false,"given":"Liu","family":"Hong","sequence":"additional","affiliation":[{"name":"School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1146\/annurev-biophys-060524-102720","article-title":"Information processing in biochemical networks","volume":"54","author":"Wolde","year":"2025","journal-title":"Annu. 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