Geometric Thermodynamics of Scallop Motion with Two Control Parameters

[2608.24158] Geometric Thermodynamics of Scallop Motion with Two Control Parameters Skip to main content Search Submit Donate Log in Condensed Matter > Statistical Mechanics arXiv:2608.24158 (cond-mat) [Submitted on 25 Aug 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Geometric Thermodynamics of Scallop Motion with Two Control Parameters Authors: Hisao Hayakawa View PDF HTML (experimental) Abstract: According to Purcell's scallop theorem, reciprocal single-degree-of-freedom shape deformations cannot achieve net propulsion in a viscous fluid. We show that this limitation is bypassed by thermal fluctuations in a two-parameter driven potential landscape. Formulating the stochastic shape dynamics via a Smoluchowski equation with position-dependent mobility $M_\mathrm{eff}(x)$, we utilize a generalized inverse operator to evaluate the slow-driving response. Cyclic modulation of the control parameters induces a non-zero Berry-Sinitsyn-Nemenman curvature $F_{12}(\bm{\theta})$, resulting in directed geometric propulsion. Simultaneously, the non-adiabatic excess dissipation is dictated by a Riemannian thermodynamic metric $g_{ij}(\bm{\theta})$. Our results provide a unified geometric foundation that bridges hydrodynamic friction, stochastic mechanics, and thermodynamic trade-offs in micro-swimmers. Comments: 24 pages (14 pages for the main text), 6 figures Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Soft Condensed Matter (cond-mat.soft) Cite as: arXiv:2608.24158 [cond-mat.stat-mech] (or arXiv:2608.24158v2 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2608.24158 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hisao Hayakawa [ view email ] [v1] Tue, 25 Aug 2026 07:17:29 UTC (2,463 KB) [v2] Fri, 28 Aug 2026 04:07:52 UTC (4,232 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2026-08 Change to browse by: cond-mat cond-mat.soft References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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