AI 中文总结
该研究基于扇贝定理，通过双参数驱动势场的热涨落绕过限制，利用Smoluchowski方程等方法实现微游泳者的定向几何推进，为相关领域提供统一几何基础。
AI 中文摘要
根据珀塞尔（Purcell）的扇贝定理，单自由度的互易形状变形无法在粘性流体中实现净推进。我们表明，在双参数驱动势场中，热涨落可绕过该限制。通过含位置依赖迁移率$M_\text{eff}(x)$的Smoluchowski方程构建随机形状动力学，利用广义逆算子评估慢驱动响应。控制参数的周期性调制诱导非零的Berry-Sinitsyn-Nemenman曲率$F_{12}(\bm{\theta})$，产生定向几何推进。同时，非绝热超额耗散由黎曼热力学度量$g_{ij}(\bm{\theta})$决定。研究结果为微游泳者的流体动力学摩擦、随机力学与热力学权衡提供了统一的几何基础。
英文摘要
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 $F_{12}(\bmθ)$, resulting in directed geometric propulsion. Simultaneously, the non-adiabatic excess dissipation is dictated by a Riemannian thermodynamic metric $g_{ij}(\bmθ)$. Our results provide a unified geometric foundation that bridges hydrodynamic friction, stochastic mechanics, and thermodynamic trade-offs in micro-swimmers.
Comments24 pages (14 pages for the main text), 6 figures
