关于类熵量$S_q$的注记（特别是对于具有粒子图像的量子系统）纯点谱模型
Remarks concerning an Entropy-like Quantity $S_q$ especially for Quantum Systems with a Particle Picture; Model with pure Point Spectra
摘要：
对于量子力学系统，定义了类熵量$S_q$。$S_q$可以不同于通常定义的熵$S$，并且对于孤立系，$S_q$可以随时间增加。$S$和$S_q$之间的区别的基本条件是假设可以由测量表示的观测量的集合{ \bf A}是自伴算子集合的真子集。基本的想法是可见的情况下，粒子系统与非平凡的散射。这种推理的模型性来自于用点谱代替连续谱。因此，很明显，$S_q$和Sinai-Kolmogorov熵之间不存在直接联系，至少在这个模型中是纯点谱。
英文摘要：
For quantum mechanical systems an entropy-like quantity $S_q$ is defined. $S_q$ can differ from the usually defined entropy $S$ and $S_q$ may increase with time for an isolated system. The essential condition for the difference between $S$ and $S_q$ is the assumption that the set {\bf A} of observables which can be represented by a measurement is a proper subset of the set of selfadjoint operators. The underlying idea is made visible in the case of particle systems with non-trivial scattering. The model-character of the reasoning comes from the fact that continuous spectra are replaced by point-spectra. So it seems evident, that no direct connection exists between $S_q$ and the Sinai-Kolmogorov-Entropy at least in this model with pure point-spectra.
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