Thermodynamic formula for the cumulant generating function of time-averaged current
Thermodynamic formula for the cumulant generating function of time-averaged current
复制标题
时均电流累积生成函数的热力学公式
DOI：
10.1103/physreve.84.061113
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Takahiro Nemoto and Shin-ichi Sasa
中科院分区：
文献类型：
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作者：
Ishihara;Shozo;Takahiro Nemoto and Shin-ichi Sasa
从运算的角度研究了时均电流的累积量产生函数。具体地说，对于非平衡条件下相互作用的布朗粒子，我们证明了累积量生成函数的一阶导数等于加了额外力的修正系统中电流的期望值，其中修正系统具有变分原理的特征。这个公式使我们想起平衡统计力学中爱因斯坦的涨落理论。此外，由于该公式在关注线性响应区域时导致波动-耗散关系，因此可以将其视为将线性响应理论推广到线性响应区域之外的有效方程。该公式也与先前已知的理论有关，如Donsker-Varadhan理论，可加性原理和最小耗散原理，但它不是由它们推导出来的。给出了它在受周期势作用的环上的驱动布朗粒子的应用实例。
The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under nonequilibrium conditions, we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory in equilibrium statistical mechanics. Furthermore, since the formula leads to the fluctuation-dissipation relation when the linear response regime is focused on, it is regarded as an extension of the linear response theory to that valid beyond the linear response regime. The formula is also related to previously known theories such as the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle, but it is not derived from them. Examples of its application are presented for a driven Brownian particle on a ring subject to a periodic potential.