论文标题
关于重复量子测量的熵产生II。例子
On entropy production of repeated quantum measurements II. Examples
论文作者
论文摘要
我们通过研究表现出各种有趣现象和奇异性的量子仪器的示例，说明了在先前工作中开发的重复量子测量过程中熵产生的数学理论。我们强调了热力学形式主义的作用，并提供了许多量子仪器的例子，这些量子仪器的概率衡量了无限序列（移位空间）的概率（较弱的）Gibbs属性。我们还讨论了与物理相关的例子，其中熵生产率满足较大的偏差原理，但未能遵守中心极限定理和波动散失定理。在整个分析中，我们探讨了与其他无关的主题，例如马尔可夫链的功能，隐藏的马尔可夫模型，矩阵产品和数字理论。
We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We emphasize the role of the thermodynamic formalism, and give many examples of quantum instruments whose resulting probability measures on the space of infinite sequences of outcomes (shift space) do not have the (weak) Gibbs property. We also discuss physically relevant examples where the entropy production rate satisfies a large deviation principle but fails to obey the central limit theorem and the fluctuation-dissipation theorem. Throughout the analysis, we explore the connections with other, a priori unrelated topics like functions of Markov chains, hidden Markov models, matrix products and number theory.
