Hurtado Pablo I, Garrido Pedro L
Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 1):041102. doi: 10.1103/PhysRevE.81.041102. Epub 2010 Apr 8.
Most systems, when pushed out of equilibrium, respond by building up currents of locally conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics. The additivity principle is a theoretical proposal that allows to compute the current distribution in many one-dimensional nonequilibrium systems. Using simulations, we validate this conjecture in a simple and general model of energy transport, both in the presence of a temperature gradient and in canonical equilibrium. In particular, we show that the current distribution displays a Gaussian regime for small current fluctuations, as prescribed by the central limit theorem, and non-Gaussian (exponential) tails for large current deviations, obeying in all cases the Gallavotti-Cohen fluctuation theorem. In order to facilitate a given current fluctuation, the system adopts a well-defined temperature profile different from that of the steady state and in accordance with the additivity hypothesis predictions. System statistics during a large current fluctuation is independent of the sign of the current, which implies that the optimal profile (as well as higher-order profiles and spatial correlations) are invariant upon current inversion. We also demonstrate that finite-time joint fluctuations of the current and the profile are well described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.
大多数系统在被推离平衡态时，会通过建立局部守恒可观测量的电流来做出响应。理解微观动力学如何决定这些电流的平均值和涨落，是非平衡统计物理学中的主要开放性问题之一。可加性原理是一种理论提议，它能够计算许多一维非平衡系统中的电流分布。通过模拟，我们在一个简单且通用的能量输运模型中验证了这一猜想，该模型既存在温度梯度，也处于正则平衡态。特别地，我们表明，正如中心极限定理所规定的那样，对于小电流涨落，电流分布呈现高斯区域；而对于大电流偏差，则呈现非高斯（指数）尾部，并且在所有情况下都遵循加拉沃蒂 - 科恩涨落定理。为了促成给定的电流涨落，系统会采用与稳态不同且符合可加性假设预测的明确温度分布。大电流涨落期间的系统统计与电流符号无关，这意味着最优分布（以及高阶分布和空间相关性）在电流反转时是不变的。我们还证明了电流和分布的有限时间联合涨落可以由可加性泛函很好地描述。这些结果表明可加性假设是计算许多非平衡系统中电流分布的一种通用且强大的工具。
