自电泳胶体链可解模型的力学与统计特性
Mechanics and statistics of a solvable model of an autophoretic colloidal chain
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中文总结 AI 辅助
本文提出一类通过单极自电泳相互作用耦合的活性胶体链可解模型，证明其存在准平衡特性，揭示耗散由平移部分承担，分析了偶极耦合对系统平衡结构的影响。
中文摘要 AI 辅助
平衡态统计力学的分析可处理性很大程度上归功于对称性：细致平衡、梯度流以及由此产生的稳态熵产生消失，这些都直接源于基础动力学的结构，而非驱动的微弱性。远离平衡态时，这类精确解十分罕见。本文中，我们识别出一类远离平衡态的活性胶体链——通过旋转-平移、自电泳（单极）相互作用耦合——其可接受精确准平衡描述：在固定链几何结构下，每个单体的取向运动方程可由标量势推导，取向部分严格满足细致平衡，而位置部分则破坏平衡结构。尽管整个系统明显受驱动且耗散，但该部分对应的稳态熵产生率（EPR）完全消失。我们对二聚体精确求解该简化动力学，对一般N聚体半解析求解，以闭式形式得到取向涨落和全系统EPR，并证明所有耗散都由平移（质心）部分承担。我们进一步研究偶极化学发射的影响——这源于单体尺度上不对称胶束沉积——发现二聚体严格保持平衡结构，而更长链则无法有此类描述。纯偶极耦合会产生真正的非平衡态，无静态吸引子，维持无固定极限的非单调漂移，且EPR本身永远无法达到稳态。单极耦合是极化态的必要且充分条件；仅偶极耦合会破坏准平衡结构，且不会被新的静态结构取代。
英文摘要
Equilibrium statistical mechanics owes much of its analytical tractability to symmetry: detailed balance, gradient flows, and the resulting vanishing of steady-state entropy production follow directly from the structure of the underlying dynamics, not from any smallness of the driving. Exact solutions of this kind are rare away from equilibrium. Here we identify a class of far-from-equilibrium active colloidal chains -- coupled via roto-translational, autophoretic (monopolar) interactions -- that admit an exact quasi equilibrium description: at fixed chain geometry, the orientational equations of motion for every monomer are derivable from a scalar potential, detailed balance holds exactly in the orientational sector, while the positional sector breaks the equilibrium structure. The associated steady-state entropy production rate (EPR) vanishes identically for this sector, even though the full system is manifestly driven and dissipative. We solve this reduced dynamics exactly for dimers and semi-analytically for general $N$-mers, obtain the orientational fluctuations and the full-system EPR in closed form, and show that all dissipation is carried by the translational (center-of-mass) sector. We further examine the effect of dipolar chemical emission -- expected from asymmetric micelle deposition at the monomer scale -- and find that the equilibrium structure holds exactly for dimers, whereas for longer chains no such description is possible. A purely dipolar coupling instead producesa genuinely non-equilibrium state with no static attractor, sustaining non-monotonic drift with no fixed limit, and an EPR that itself never reaches steady state. Monopolar coupling remains necessary and sufficient for the polarized state; dipolar coupling alone breaks the quasi-equilibrium structure without replacing it with a new static one.
