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

[2311.16569] Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Statistical Mechanics arXiv:2311.16569 (cond-mat) [Submitted on 28 Nov 2023 ( v1 ), last revised 11 Nov 2024 (this version, v3)] Title: Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation Authors: Ryuna Nagayama , Kohei Yoshimura , Artemy Kolchinsky , Sosuke Ito View a PDF of the paper titled Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation, by Ryuna Nagayama and 3 other authors View PDF 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 (EPR) based on the orthogonality of thermodynamic forces, in this way identifying the amount of dissipation caused by each factor. This enables us to extract the excess EPR that genuinely contributes to the time evolution of patterns. We also show that a similar geometric method further decomposes the EPR into detailed contributions, e.g., the dissipation from each point in real or wavenumber space. Second, we relate the excess EPR 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 EPR 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 it 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. Comments: 49 pages, 11 figures Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Pattern Formation and Solitons (nlin.PS) Cite as: arXiv:2311.16569 [cond-mat.stat-mech] (or arXiv:2311.16569v3 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2311.16569 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1103/PhysRevResearch.7.033011 Focus to learn more DOI(s) linking to related resources Submission history From: Ryuna Nagayama [ view email ] [v1] Tue, 28 Nov 2023 07:26:08 UTC (1,535 KB) [v2] Tue, 12 Dec 2023 04:35:56 UTC (1,536 KB) [v3] Mon, 11 Nov 2024 07:20:03 UTC (1,392 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation, by Ryuna Nagayama and 3 other authors View PDF TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2023-11 Change to browse by: cond-mat nlin nlin.PS References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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