The purpose of the present paper is to study the entropy h_s(Φ) of a quantum dynamical systems Φ=(L,s,φ),where s is a bayessian state on an orthomodular lattice L.Having introduced the notion of entropy hs(φ,)of p...The purpose of the present paper is to study the entropy h_s(Φ) of a quantum dynamical systems Φ=(L,s,φ),where s is a bayessian state on an orthomodular lattice L.Having introduced the notion of entropy hs(φ,)of partition of a Boolean algebra B with respect to a state s and a state preserving homomorphism φ,we prove afew results on that,define the entropy of a dynamical system h_s(Φ),and show its invarianee.The concept of sufficientfamilies is also given and we establish that hs(Φ) comes out to be equal to the supremum of h_s(φ,),where variesover any sufficient family.The present theory has then been extended to the quantum dynamical system ( L,s,φ),whichas an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system(B,s_o,φ),where B is a Boolean algebra and so is a state on B.展开更多
文摘The purpose of the present paper is to study the entropy h_s(Φ) of a quantum dynamical systems Φ=(L,s,φ),where s is a bayessian state on an orthomodular lattice L.Having introduced the notion of entropy hs(φ,)of partition of a Boolean algebra B with respect to a state s and a state preserving homomorphism φ,we prove afew results on that,define the entropy of a dynamical system h_s(Φ),and show its invarianee.The concept of sufficientfamilies is also given and we establish that hs(Φ) comes out to be equal to the supremum of h_s(φ,),where variesover any sufficient family.The present theory has then been extended to the quantum dynamical system ( L,s,φ),whichas an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system(B,s_o,φ),where B is a Boolean algebra and so is a state on B.
