An exact response theory has recently been developed within the field of Nonequilibrium Molecular Dynamics. Its main ingredient is known as the Dissipation Function, Ω. This quantity determines nonequilbrium properties like thermodynamic potentials do with equilibrium states. In particular, Ω can be used to determine the exact response of particle systems obeying classical mechanical laws, subjected to perturbations of arbitrary size. Under certain conditions, it can also be used to express the response of a single system, in contrast to the standard response theory, which concerns ensembles of identical systems. The dimensions of Ω are those of a rate, hence Ω can be associated with the entropy production rate, provided local thermodynamic equilibrium holds. When this is not the case for a particle system, or generic dynamical systems are considered, Ω can equally be defined, and it yields formal, thermodynamic-like, relations. While such relations may have no physical content, they may still constitute interesting characterizations of the relevant dynamics. Moreover, such a formal approach turns physically relevant, because it allows a deeper analysis of Ω and of response theory than possible in case of fully fledged physical models. Here, we investigate the relation between linear and exact response, pointing out conditions for the validity of the response theory, as well as difficulties and opportunities for the physical interpretation of certain formal results.

中文翻译：

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耗散函数：非平衡物理和动力系统

最近在非平衡分子动力学领域发展了一种精确响应理论。它的主要成分被称为耗散函数，Ω。这个量决定了非平衡特性，就像热力学势对平衡状态所做的那样。特别是，Ω 可用于确定服从经典力学定律的粒子系统的准确响应，受到任意大小的扰动。在某些条件下，它也可以用来表达单个系统的响应，与标准响应理论相反，标准响应理论涉及相同系统的集合。Ω 的维数是速率的维数，因此 Ω 可以与熵产生率相关联，前提是局部热力学平衡成立。当粒子系统不是这种情况时，或通用动力系统被考虑，Ω 可以同样被定义，并且它产生形式的、类似热力学的关系。虽然这种关系可能没有物理内容，但它们仍然可能构成相关动态的有趣特征。此外，这种形式化方法与物理相关，因为与完全成熟的物理模型相比，它允许对 Ω 和响应理论进行更深入的分析。在这里，我们研究线性响应和精确响应之间的关系，指出响应理论有效性的条件，以及对某些形式结果进行物理解释的困难和机会。它们可能仍然构成相关动态的有趣特征。此外，这种形式化方法与物理相关，因为与完全成熟的物理模型相比，它允许对 Ω 和响应理论进行更深入的分析。在这里，我们研究线性响应和精确响应之间的关系，指出响应理论有效性的条件，以及对某些形式结果进行物理解释的困难和机会。它们可能仍然构成相关动态的有趣特征。此外，这种形式化方法与物理相关，因为与完全成熟的物理模型相比，它允许对 Ω 和响应理论进行更深入的分析。在这里，我们研究线性响应和精确响应之间的关系，指出响应理论有效性的条件，以及对某些形式结果进行物理解释的困难和机会。