The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally-relevant model of such a system -- the so-called Brownian gyrator -- a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under non-equilibrium conditions, while no net rotation takes place in equilibrium. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components, but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in non-equilibrium. We show that indeed one can conclusively distinguish between equilibrium and non-equilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a non-equilibrium dynamics.
Destructive effect of fluctuations on the performance of a Brownian gyrator
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600)（凝聚态物质理论物理实验室）；Physics Department, Univer（物理学系，大学）
Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
通过与标量势$V(\vec r)$和矢量势$\vec A(\vec r)$中的非厄米量子力学的对应，重新讨论了在$N$维的任意力场$\vec f(\vec r)$中的非平衡Fokker-Planck动力学.不可逆性的相关参数是$\frac{N(N-1)}{2}$磁矩阵元$B_{nm}(\vec x ) =-B_{mn} (\vec x ) = \partial_n A_m (\vec x ) - \partial_m A_n (\vec x )$，而探索矢量势$\vec A(\vec r) $的相应规范变换是有启发性的。这种量子解释对于研究随机轨道的所有时间可加观测量的统计更有成效，因为它们的生成函数对应于具有附加标量和/或矢量势的相同量子问题。我们的主要结论是，分析其大偏差的性质和相应的Doob条件过程的建设可以大大简化通过选择一个适当的规范为每一个目的。这个一般的框架，然后应用到特殊的时间添加剂的观测量的奥恩斯坦-乌伦贝克轨迹在维度$N$，其生成函数对应于量子传播涉及二次标量势和线性矢量势，即量子谐振子在恒定的磁性矩阵。作为简单的说明性例子，我们最后集中在布朗回转器的尺寸$N=2$，以计算其随机轨迹的熵产生的大偏差性质，并构造相应的条件过程具有给定的值的熵产生每单位时间。
Istituto dei Sistemi Complessi - Consiglio Nazionale delle Ricerche（复杂系统研究所-意大利国家研究委员会）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；INFN, Sezione Roma2（意大利国家核物理研究所罗马第二分部）
