不可逆确定性动力学的平衡、涨落关系和输运
Equilibrium, fluctuation relations and transport for irreversible deterministic dynamics
摘要：
在最近的一篇论文[M。科兰杰利\textit{et al.}，J.统计。机械师P04021，（2011）]认为相空间收缩率$Λ$的波动关系可以适当地扩展到不可逆耗散系统。我们在这里加强这些论点，提供一个简单的不可逆非平衡面包师模型的属性的基础上的分析和数值证据。我们还考虑了响应问题，表明输运系数不受微观动力学不可逆性的影响。此外，我们证明了一种形式的\textit{detailed balance}，因此平衡，持有相关变量的空间，尽管不可逆的相空间动态。这证实了这样一种观点，即由投影到相关坐标的子空间上产生的相同的随机描述与完全不同的基本确定性动力学是相容的。换句话说，微观动力学的细节在很大程度上与涨落关系、平衡行为和对扰动的响应等性质无关。
英文摘要：
In a recent paper [M. Colangeli \textit{et al.}, J.\ Stat.\ Mech.\ P04021, (2011)] it was argued that the Fluctuation Relation for the phase space contraction rate $Λ$ could suitably be extended to non-reversible dissipative systems. We strengthen here those arguments, providing analytical and numerical evidence based on the properties of a simple irreversible nonequilibrium baker model. We also consider the problem of response, showing that the transport coefficients are not affected by the irreversibility of the microscopic dynamics. In addition, we prove that a form of \textit{detailed balance}, hence of equilibrium, holds in the space of relevant variables, despite the irreversibility of the phase space dynamics. This corroborates the idea that the same stochastic description, which arises from a projection onto a subspace of relevant coordinates, is compatible with quite different underlying deterministic dynamics. In other words, the details of the microscopic dynamics are largely irrelevant, for what concerns properties such as those concerning the Fluctuation Relations, the equilibrium behaviour and the response to perturbations.
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