随机矩阵的粗粒化伸缩
Dilation of stochastic matrices by coarse graining
摘要：
我们考虑两种不同的方式表示随机矩阵的双随机的一个更大的概率空间，被称为“膨胀均匀粗粒化”和“环境膨胀”。后者的动机是类比量子理论中的操作膨胀。这两种类型的膨胀都可以被看作是一般“粗粒化膨胀”的特殊情况。我们还讨论了熵平衡，并说明我们的结果，除其他外，随机$4\times 4$ -矩阵，它作为一个简化的模型的麦克斯韦恶魔的条件行动的一个例子。
英文摘要：
We consider two different ways of representing stochastic matrices by bi-stochastic ones acting on a larger probability space, referred to as ``dilation by uniform coarse graining" and ``environmental dilation". The latter is motivated by analogy to the dilation of operations in quantum theory. Both types of dilation can be viewed as special cases of a general ``dilation by coarse graining". We also discuss the entropy balance and illustrate our results, among others, by an example of a stochastic $4\times 4$-matrix, which serves as a simplified model of the conditional action of Maxwell's demon.
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