Departamento de Electromagnetismo y Física de la Materia, and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain.
Proc Natl Acad Sci U S A. 2011 May 10;108(19):7704-9. doi: 10.1073/pnas.1013209108. Epub 2011 Apr 14.
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.
波动普遍存在于自然界中，反映了宏观层面上离散的微观世界。尽管它们起源于明显的噪声，但波动编码了当前系统物理学的基本方面，对于理解不可逆性和非平衡行为至关重要。为了维持给定的波动，系统在相空间中穿越一条精确的最优路径。在这里，我们表明，通过要求最优路径在对称变换下保持不变，可以揭示新的、普遍的、任意远离平衡的波动关系。这通过将对称原理引入波动领域，为深入理解非平衡物理学开辟了一条未探索的途径。我们通过研究非平衡时的电流分布的对称性来阐明这个概念。特别是，我们推导出了一个等距波动关系，以一种惊人的简单方式将任何一对等距电流波动的概率联系起来。这个关系源于动力学的时间可逆性，包括在这种情况下 Gallavotti-Cohen 波动定理，但为时间可逆性对非平衡波动统计施加的高水平对称性提供了一个全新的视角。新的对称性意味着电流累积量和非线性响应系数的方程存在显著的层次结构，远远超出了 Onsager 的互易关系和 Green-Kubo 公式。我们在广泛的数值模拟中验证了新对称性关系的有效性，并提出波动中的对称性思想作为最优路径不变性具有广泛的影响，涉及到许多领域。
