Bonança Marcus V S
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Sep;78(3 Pt 1):031107. doi: 10.1103/PhysRevE.78.031107. Epub 2008 Sep 5.
A derivation of the fluctuation-dissipation theorem for the microcanonical ensemble is presented using linear response theory. The theorem is stated as a relation between the frequency spectra of the symmetric correlation and response functions. When the system is not in the thermodynamic limit, this result can be viewed as an extension of the fluctuation-dissipation relations to a situation where dynamical fluctuations determine the response. Therefore, the relation presented here between equilibrium fluctuations and response can have a very different physical nature from the usual one in the canonical ensemble. These considerations imply that the fluctuation-dissipation theorem is not restricted to the context of the canonical ensemble, where it is usually derived. Dispersion relations and sum rules are also obtained and discussed in the present case. Although analogous to the Kramers-Kronig relations, they are not related to the frequency spectrum but to the energy dependence of the response function.
利用线性响应理论给出了微正则系综涨落耗散定理的一种推导。该定理表述为对称关联函数和响应函数的频谱之间的一种关系。当系统不在热力学极限时，这一结果可视为涨落耗散关系向动力学涨落决定响应的情形的一种推广。因此，这里给出的平衡涨落与响应之间的关系可能具有与正则系综中通常情形非常不同的物理性质。这些考虑意味着涨落耗散定理并不局限于通常推导它的正则系综的情形。在当前情形下还得到并讨论了色散关系和求和规则。尽管类似于克拉默斯 - 克勒尼希关系，但它们与频谱无关，而是与响应函数的能量依赖性有关。
