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Relative Entropy and Entropy Production for Equilibrium States in pAQFT

机译：PAQT中的均衡状态相对熵和熵产生

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摘要

We analyze the relative entropy of certain KMS states for scalar self-interacting quantum field theories over Minkowski backgrounds that have been recently constructed by Fredenhagen and Lindner (Commun Math Phys 332:895, 2014) in the framework of perturbative algebraic quantum field theory. The definition we are using is a generalization of the Araki relative entropy to the case of field theories. In particular, we shall see that the analyzed relative entropy is positive in the sense of perturbation theory; hence, even if the relative modular operator is not at disposal in this context, the proposed extension is compatible with perturbation theory. In the second part of the paper, we analyze the adiabatic limits of these states, showing that also the density of relative entropy obtained dividing the relative entropy by the spatial volume of the region where interaction takes place is positive and finite. In the last part of the paper, we discuss the entropy production for states obtained by an ergodic mean (time average) of perturbed KMS states evolved with the free evolution recently constructed by the authors of the present paper. We show that their entropy production vanishes even if return to equilibrium (Haag et al. in Commun Math Phys 38:173-193, 1974; Robinson in Commun Math Phys 31:171-189, 1973) does not hold. This means that states constructed in this way are thermodynamically simple, namely they are not so far from equilibrium states.
机译：我们分析了SCINKSKI背景的SCINKSKI背景的标量的相对熵，这些概况最近由FREDENHAGEN和LINDNER（MATH MATOM 332：895,2014）在扰动代数量子领域理论框架中构建的。我们使用的定义是Araaki相对熵的概括到野外理论的情况。特别是，我们将看到分析的相对熵在扰动理论意义上是积极的;因此，即使在这种情况下相对模块化操作员未处置，所提出的延伸率也与扰动理论兼容。在本文的第二部分中，我们分析了这些状态的绝热界限，表明，所获得的相对熵的密度除以相互作用的区域的空间体积分割相对熵的相对熵是正的和有限的。在本文的最后一部分中，我们讨论了通过本文最近构建的自由演进的erbodic均值（时间平均值）所获得的ergodic平均值（时间平均值）所获得的熵产生。我们表明，即使返回均衡（Haag等人，他们的熵产量也消失了（Haag等人。这意味着以这种方式构建的状态是热力学上简单的，即它们不是远离均衡状态。

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