Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation

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• dc.contributor.author Nagayama, Ryuna
• dc.contributor.author Yoshimura, Kohei
• dc.contributor.author Kolchinsky, Artemy
• dc.date.accessioned 2025-09-09T06:33:39Z
• dc.date.available 2025-09-09T06:33:39Z
• dc.date.issued 2025
• dc.description.abstract We establish universal relations between pattern formation and dissipation with a geometric approach to nonequilibrium thermodynamics of deterministic reaction-diffusion systems. We first provide a way to systematically decompose the entropy production rate based on the orthogonality of thermodynamic forces, thereby identifying the amount of dissipation caused by each factor. This enables us to extract the excess entropy production rate that genuinely contributes to the time evolution of patterns. We also show that a similar geometric method further decomposes the entropy production rate into detailed contributions, e.g., the dissipation from each point in real or wavenumber space. Second, we relate the excess entropy production rate to the details of the change in patterns through two types of thermodynamic trade-off relations for reaction-diffusion systems: thermodynamic speed limits and thermodynamic uncertainty relations. The former relates dissipation and the speed of pattern formation, and the latter bounds the excess entropy production rate with partial information on patterns, such as specific Fourier components of concentration distributions. In connection with the derivation of the thermodynamic speed limits, we also extend optimal transport theory to reaction-diffusion systems, which enables us to measure the speed of the time evolution. This extension of optimal transport also solves the minimization problem of the dissipation associated with the transition between two patterns, and constructs energetically efficient protocols for pattern formation. We numerically demonstrate our results using chemical traveling waves in the Fisher–Kolmogorov–Petrovsky–Piskunov equation and changes in symmetry in the Brusselator model. Our results apply to general reaction-diffusion systems and contribute to understanding the relations between pattern formation and unavoidable dissipation.en
• dc.description.sponsorship The authors thank Naruo Ohga for fruitful discussions on thermodynamic bounds. K.Y., A.K., and S.I. thank Andreas Dechant for fruitful discussions on the geometric decomposition. R.N. thanks Yasushi Okada for fruitful discussions on thermodynamics of RDSs. S.I. thanks Masafumi Oizumi and Daiki Sekizawa for fruitful discussions on the geometric decomposition. This research was supported by JSR Fellowship, the University of Tokyo. K.Y. is supported by Grant-in-Aid for JSPS Fellows Grant No. 22J2161. A.K. received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 101068029 and support from Grant 62417 from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. S.I. is supported by JSPS KAKENHI Grants No. 19H05796, No. 21H01560, No. 22H01141, No. 23H00467, and No. 24H00834, JST ERATO Grant No. JPMJER2302, and UTEC-UTokyo FSI Research Grant Program.en
• dc.format.mimetype application/pdf
• dc.identifier.citation Nagayama R, Yoshimura K, Kolchinsky A, Ito S. Geometric thermodynamics of reaction-diffusion systems: thermodynamic trade-off relations and optimal transport for pattern formation. Phys Rev Research. 2025 Jul-Sep;7(3):033011. DOI: 10.1103/PhysRevResearch.7.033011
• dc.identifier.doi http://dx.doi.org/10.1103/PhysRevResearch.7.033011
• dc.identifier.issn 2643-1564
• dc.identifier.uri http://hdl.handle.net/10230/71165
• dc.language.iso eng
• dc.publisher American Physical Society
• dc.relation.ispartof Physical Review Research. 2025 Jul-Sep;7(3):033011
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/101068029
• dc.rights Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Published by the American Physical Society
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.other Termodinàmicaca
• dc.subject.other Equilibri termodinàmicca
• dc.subject.other Termodinàmica del desequilibrica
• dc.title Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formationen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion