English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider some questions concerning the monotonicity properties of entropyand mean entropy of states on translationally invariant systems (classicallattice, quantum lattice and quantum continuous). By taking the property ofstrong subadditivity, which for quantum systems was proven rather late in thehistorical development, as one of four primary axioms (the other three beingsimply positivity, subadditivity and translational invariance) we are able toobtain results, some new, some proved in a new way, which appear to complementin an interesting way results proved around thirty years ago on limiting meanentropy and related questions. In particular, we prove that as the sizes ofboxes in Z^n or R^n increase in the sense of set inclusion, (1) their meanentropy decreases monotonically and (2) their entropy increases monotonically.Our proof of (2) uses the notion of "m-point correlation entropies" which weintroduce and which generalize the notion of "index of correlation" (see e.g.R. Horodecki, Phys. Lett. A 187 p145 1994). We mention a number of furtherresults and questions concerning monotonicity of mean entropy for more generalshapes than boxes and for more general translationally invariant (/homogeneous)lattices and spaces than Z^n or R^n.Comment: 17 pages, LaTeX, uses amsmath, amsfonts, latexsym, amssymb and amsthm  usepackages; 2 LaTeX figures, uses curves usepackage. Submitted to "Journal  of Mathematical Physics

Monotonicity with volume of entropy and of mean entropy for translationally invariant systems as consequences of strong subadditivity