We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while quantum systems can be considered the ones where the internal dynamics cannot be accessed at all. As information entropy can be used to characterize how much the state of the whole system identifies the state of its parts, classical systems can have arbitrarily small information entropy while quantum systems cannot. This provides insights that allow us to understand the analogies and differences between the two theories.

中文翻译：

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经典哈密顿力学、量子力学和信息熵之间的基本联系

我们表明，经典系统和量子系统之间的主要区别可以用信息熵来理解。可以将经典系统视为可以以任意精度知道内部动力学的系统，而可以将量子系统视为根本无法访问内部动力学的系统。由于信息熵可以用来表征整个系统的状态在多大程度上识别了其各个部分的状态，因此经典系统可以具有任意小的信息熵，而量子系统则不能。这提供了使我们能够理解这两种理论之间的类比和差异的见解。