2007/01/06 by Anilesh Mohari, Mohari, Anilesh
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.math/0701186
openalex publication_date 2007/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \IM =⊗n ∈ \IZ M(n)(\IC) be the two sided infinite tensor product C^*-algebra of d dimensional matrices M(n)(\IC)= Md(\IC) over the field of complex numbers \IC. Let ω be a translation invariant state of \IM. In a recent paper, we have proved that the mean entropy s(ω) is a complete invariant for certain classes of translation invariant state ω of \IM. In this paper, we have developed a general theory for dynamical entropy for an automorphism on an arbitrary C^*- or von-Neumann algebras based on repeated admissible measurement processes. In particular, we prove that dynamical entropy hω(θ) for translation dynamics (\IM,θ,ω) satisfies s(ω) ≤ hω(θ) ≤ 2s(ω). In case ω is an infinite tensor product state of \IM then hω(θ)=s(ω).