标题： 混沌非哈密顿系统的涨落-耗散关系 显示英文标题

标题： Fluctuation-dissipation relation for chaotic non-Hamiltonian systems

摘要： 在耗散动力系统中，相空间体积平均上会收缩。 因此，吸引子上的不变测度相对于勒贝格测度是奇异的。 正如Ruelle所指出的，一般的扰动会将状态推出吸引子，因此扰动的统计特征，特别是松弛的统计特征，不能仅通过吸引子上的未扰动动力学来理解。 这一观点似乎严重限制了标准涨落-耗散过程在非平衡（耗散）系统统计力学中的适用性。 在本文中，我们表明，在具有许多自由度的系统中，稳态的奇异特性并不构成严重的限制。 原因是通常处理的是投影动力学，这些动力学在相应的低维空间中与正则的概率分布相关联。 显示英文摘要

摘要： In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the state out of the attractor, hence the statistical features of the perturbation and, in particular, of the relaxation, cannot be understood solely in terms of the unperturbed dynamics on the attractor. This remark seems to seriously limit the applicability of the standard fluctuation dissipation procedure in the statistical mechanics of nonequilibrium (dissipative) systems. In this paper we show that the singular character of the steady state does not constitute a serious limitation in the case of systems with many degrees of freedom. The reason is that one typically deals with projected dynamics, and these are associated with regular probability distributions in the corresponding lower dimensional spaces.