Belousov Roman, Cohen E G D
The Rockefeller University, New York, New York 10065, USA.
The Rockefeller University, New York, New York 10065, USA and Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, USA.
Phys Rev E. 2016 Dec;94(6-1):062124. doi: 10.1103/PhysRevE.94.062124. Epub 2016 Dec 19.
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an analytical expression for the time autocorrelation function of a general fluctuating quantity. This theoretical result is then tested in a study of a shear flow by molecular dynamics simulations. The proposed form of the time autocorrelation function yields an excellent fit to our computational data for both equilibrium and nonequilibrium steady states. Unlike the analogous result of the first-order Onsager-Machlup theory, our expression correctly describes the short-time correlations. Its utility is demonstrated in an application of the Green-Kubo formula for the transport coefficient. Curiously, the normalized time autocorrelation function for the shear flow, which only depends on the deterministic part of the fluctuation dynamics, appears independent of the external shear force in the linear nonequilibrium regime.
通过运用空间不对称系统朗之万动力学的最新进展，我们常规性地推广了时间二阶的昂萨格 - 马赫卢普涨落理论。以这种形式，它适用于平衡态以及非平衡稳态下的涨落变量，包括流体动力学流。从所得到的随机方程的解中，我们推导出了一般涨落量的时间自相关函数的解析表达式。然后在一项通过分子动力学模拟对剪切流的研究中检验了这一理论结果。所提出的时间自相关函数形式对我们关于平衡态和非平衡稳态的计算数据都给出了极佳的拟合。与一阶昂萨格 - 马赫卢普理论的类似结果不同，我们的表达式正确地描述了短时间相关性。其效用在格林 - 库博输运系数公式的应用中得到了证明。奇怪的是，仅取决于涨落动力学确定性部分的剪切流归一化时间自相关函数，在线性非平衡区域中似乎与外部剪切力无关。
