On the origin and the use of fluctuation relations for the entropy
On the origin and the use of fluctuation relations for the entropy
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论熵涨落关系的起源和运用
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
C. Maes
中科院分区：
文献类型：
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作者：
C. Maes
近十年来，人们已经推导和分析了各种关于熵产生的涨落关系。这些关系涉及时间反转下的熵产生的对称性，并被认为是涨落-耗散关系的非微扰推广。我描述了一个统一的框架来理解这些关系，并提出了一个算法来派生它们。这些涨落关系都源于主要的观测结果，即在很大程度上，依赖于路径的熵产生是时空历史上拉格朗日中时间反转破缺的源项。这是通过大量的例子和一般的理论论证来说明的。我把这些关系从它们产生的严格的动力学背景中移开，把它们带回统计力学的背景中，在统计力学的背景下，熵在玻尔兹曼意义上被理解为测量明显条件的典型性。我讨论了功和自由能之间的关系是如何自然地放在这个框架中的，以及暂态和稳态涨落定理是如何简单的结果。熵产生的涨落对称性通常只在大时间内渐近有效，这使得它们大多无法进行实验验证，而最近有人声称，它们将有效地量化违反第二定律的情况。对由此产生的涨落对称性感兴趣的部分原因是，它们是如此普遍有效，这在非平衡统计力学中是罕见的。然而，它们并不为响应函数提供系统的扰动展开。为此，我们需要回到完整的拉格朗日量，并考虑对其时间对称部分的非平衡修改。
Since about a decade various fluctuation relations for the entropy production have been derived and analyzed. These relations deal with symmetries of the entropy production under time-reversal and have been proposed as a non-perturbative generalization of fluctuation–dissipation relations. I describe a unifying framework for understanding these relations and I present an algorithm to derive them. The fluctuation relations all follow from the main observation that in great generality the pathdependent entropy production is the source-term of time-reversal breaking in the Lagrangian over space-time histories. That is illustrated via a number of examples as well as via a general theoretical argument. I move these relations away from the strict dynamical background in which they originated and take them back to the context of statistical mechanics where entropy is understood in the sense of Boltzmann, as measuring the typicality of a manifest condition. I discuss how a relation between work and free energy is naturally put in that framework and how the transient and steady state fluctuation theorems are simple consequences. The fact that fluctuation symmetries for the entropy production are in general only valid asymptotically for large times, makes them mostly inaccessible for experimental verification, in contrast with a recent claim that they would usefully quantify second law violations. Part of the interest in the resulting fluctuation symmetries is that they are so universally valid, a rare occasion in nonequilibrium statistical mechanics. However they do not provide a systematic perturbation expansion for response functions. For that one needs to go back to the full Lagrangian and also consider the nonequilibrium modifications to its time-symmetric part.