AI 中文总结
该研究明确奇扩散系统的反常关联仅源于奇迁移率，其状态依赖可观测量统计可通过常规朗之万动力学计算，相关普适关系仍有效，且通过多种系统验证了结论。
AI 中文摘要
奇扩散率是一种横向输运系数，出现在时间反演对称性和宇称对称性被破坏的情形下，其最显著的特征是由扩散张量的反对称部分产生的垂直于密度梯度的概率通量。本文证明，对于在任意时刻测量的任意数量依赖状态的可观测量，它们的联合统计与扩散张量的反对称部分无关，因此洛伦兹通量不会对任何多点状态-可观测量测量产生贡献。该结果阐明了涨落-耗散关系通常关联的两种效应的不同作用，即奇迁移率与奇扩散率，这一观察表明奇扩散系统中的反常关联完全源于奇迁移率；同时，这使得在保留反对称迁移率张量的情况下，可使用不含反对称扩散部分的常规朗之万动力学计算奇扩散系统中依赖状态的可观测量的统计，这意味着仅与依赖状态的可观测量相关的普适关系，如非线性涨落-耗散关系和广义格林-久保关系，在奇扩散系统中无需修改仍有效。我们通过平均反向弛豫、扩散系数、非线性涨落-耗散关系以及不同系统中的广义格林-久保关系验证了上述发现。
英文摘要
Odd diffusivity is a transverse transport coefficient that appears when time-reversal and parity symmetries are broken. Its most distinctive signature is a probability flux perpendicular to a density gradient, generated by the antisymmetric part of the diffusion tensor. Here we show that for an arbitrary number of state-dependent observables measured at arbitrary times, their joint statistics are independent of the antisymmetric part of the diffusion tensor. Thus, the Lorentz flux does not contribute to any multipoint state-observable measurements. The result clarifies the separate roles of two effects that are often linked together by fluctuation--dissipation relations, i.e., odd mobility and odd diffusivity. This observation demonstrates that the anomalous correlations in odd-diffusive systems originate solely from odd mobility. It also allows the statistics of state-dependent observables in odd-diffusive systems to be computed using conventional Langevin dynamics without the antisymmetric diffusion part while preserving the antisymmetric mobility tensor. It implies that universal relations associated with state-dependent observables alone, such as nonlinear fluctuation--dissipation relations and generalized Green--Kubo relations, remain valid in odd-diffusive systems without modification. We verify our findings through mean back relaxation, the diffusion coefficient, the nonlinear fluctuation--dissipation relation, and a generalized Green--Kubo relation in diverse systems.
Comments15 pages, 4 figures
