代数熵与时间之箭
Algebraical Entropy and Arrow of Time
摘要：
一般认为，时间的不可逆性只出现在宏观物理学中。在这里，我们试图引入时间的微观物理箭头，假设在基本层面上，自然可以是非关联的。在非关联的情况下，获得测量的数值结果，这需要至少三个成分：对象，设备和观察者，取决于操作的顺序，是模糊的。我们表明，使用八元数作为一个基本代数，在任何测量，导致产生不可避免的18.6位相对熵的概率密度函数的主动和被动的转换，这对应于组G2和SO（7），分别。这种代数熵可以用来确定时间的箭头，类似于热力学熵。
英文摘要：
Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical results of a measurement, which requires at least three ingredients: object, device and observer, in the non-associative case depends on ordering of operations and is ambiguous. We show that use of octonions as a fundamental algebra, in any measurement, leads to generation of unavoidable 18.6~bit relative entropy of the probability density functions of the active and passive transformations, which correspond to the groups G2 and SO(7), respectively. This algebraical entropy can be used to determine the arrow of time, analogically as thermodynamic entropy does.
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