经典系统的广义涨落定理
Generalized fluctuation theorems for classical systems
摘要：
涨落定理在研究物理系统的非平衡动力学中有着特殊的地位。最广泛使用的形式是加拉沃蒂-科恩涨落定理，它是根据工作的分布$p(W)/p(-W)=\exp(αW)$。本文导出了任意高斯马氏过程的涨落定理的一般形式，并找到了参数$α$成为普适参数$1/kT$的条件.作为应用，我们考虑抛物势场中电子经典回旋运动的涨落定理。电子的运动由四个耦合的朗之万方程描述，因此是非平凡的。推广的定理对非平衡定常状态同样有效。
英文摘要：
Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\exp(αW)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $α$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.
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