非平衡微米尺度系统中的涨落与响应
Fluctuations and response in a non-equilibrium micron-sized system
摘要：
具有马尔可夫动力学的非平衡系统的线性响应满足由涨落的时间对称性和反对称性导出的广义涨落耗散关系。该关系涉及感兴趣的可观测量的两个关联函数的总和：一个具有熵过剩，第二个具有相对于未扰动过程的动力学活动过剩，除了系统的动力学之外不依赖于任何东西。我们说明这种方法在实验测定的线性响应的势能的布朗粒子在环形光阱。过阻尼粒子运动被有效地限制在一个圆上，经历一个周期势，并被一个非保守力驱动而脱离平衡。在这个简单的实验系统中进行独立的直接和间接测量的非平衡稳态附近的线性响应。同样的想法也适用于测量浸入牛顿流体中的更一般的非平衡微米尺寸系统的响应，无论是静止状态还是非静止状态，并且可能包括惯性自由度。
英文摘要：
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two correlation functions of the observable of interest: one with the entropy excess and the second with the excess of dynamical activity with respect to the unperturbed process, without recourse to anything but the dynamics of the system. We illustrate this approach in the experimental determination of the linear response of the potential energy of a Brownian particle in a toroidal optical trap. The overdamped particle motion is effectively confined to a circle, undergoing a periodic potential and driven out of equilibrium by a non-conservative force. Independent direct and indirect measurements of the linear response around a non-equilibrium steady state are performed in this simple experimental system. The same ideas are applicable to the measurement of the response of more general non-equilibrium micron-sized systems immersed in Newtonian fluids either in stationary or non-stationary states and possibly including inertial degrees of freedom.
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