Entropy Densities for Algebraic States
Entropy Densities for Algebraic States
复制标题
代数态的熵密度
DOI：
10.1006/jfan.1994.1125
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发表时间：
1994
影响因子：
1.7
通讯作者：
D. Petz
中科院分区：
文献类型：
--
作者：
F. Hiai;D. Petz
摘要代数关联态是无限张量积C ~*-代数上的量子不变态，它的构造是相当一般的，包括量子马尔可夫链。对于强混合代数态，我们得到了平均熵与另一种熵密度之间的关系，即在统计力学意义下相应态下的宏观均匀性。为了这个目的，一个突出的属性近似产品型强混合代数状态。当参考态为强混合代数态时，我们也得到了两个双不变态的平均相对熵与其它熵密度的类似关系。
Abstract Algebraic (or finitely correlated) states are translation-invariant states on an infinite tensor product C *-algebra, whose construction is rather general, including quantum Markov chains. For a strongly mixing algebraic state, we obtain the relation between the mean entropy and another entropy density, which means the macroscopic uniformity under the relevant state in the statistical mechanical sense. For this purpose an outstanding property of approximately product type is shown for strongly mixing algebraic states. We also obtain similar relations of the mean relative entropy to other entropy densities for two translation-invariant states when the reference one is a strongly mixing algebraic state.