Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State  

作　　者：Mona Khare Shraddha Roy 

机构地区：[1]Department of Mathematics,University of Allahabad,Allahabad,211 001,India [2]Allahabad Mathematical Society,10,C.S.P.Singh Marg,Allahabad,211 001,India

出　　处：《Communications in Theoretical Physics》2008年第9期551-556,共6页理论物理通讯（英文版）

摘　　要：The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.

关 键 词：orthomodular lattices quantum logic valuation ISOMORPHISM PARTITIONS ENTROPY quantum dynamical systems sufficient families 

分 类 号：O413[理学—理论物理]