Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State
Mona Khare, Shraddha Roy · Communications in Theoretical Physics · 2008
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 h s (ϕ, ) of partition of a Boolean algebra B with respect to a state s and a state preserving homomorphism ϕ, we prove a few results on that, define the entropy of a dynamical system h s (Φ), and show its invariance. The concept of sufficient families is also given and we establish that h s (Φ) comes out to be equal to the supremum of h s (ϕ, ), where varies over any sufficient family. The present theory has then been extended to the quantum dynamical system (L,s,ϕ), which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system (B,s 0 ,ϕ), where B is a Boolean algebra and s 0 is a state on B.