Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 7th 2021

    I have added

    • Paolo Facchi, Giovanni Gramegna, Arturo Konderak, Entropy of quantum states (arXiv:2104.12611)

    and added publication details to

    • A. P. Balachandran, T. R. Govindarajan, Amilcar R. de Queiroz, A. F. Reyes-Lega, Algebraic approach to entanglement and entropy, Phys. Rev. A 88, 022301 (2013) (arXiv:1301.1300)

    and grouped together more discernibly the references on operator-algebraic entropy

    diff, v50, current

  1. Fixed a broken link in the references.

    Rongmin Lu

    diff, v55, current

  2. Added details to a reference.

    Rongmin Lu

    diff, v57, current

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeAug 15th 2022
    Although the formula for the entropy of an Algebra is correct (or at least consistent with the definition of Peter Walters "An introduction to Ergodic Theory" ),
    subsequent link to density distribution entropy is incorrect.
    Indeed, one can readily check that the entropy for any density distribution computed with this definition is infinite.
    One can also see that entropy with this definition is an invariant of the measured sigma algebra. It thus yield the same value for every probability space isomorphic to R (with standard algebra and measure). This includes all density distributions of any dimensions.

    In particular the statement that this entropy is equal to the entropy relatively to Lebesgues measure writtent here as an integral of f(x)*log(f(x)) is false.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 15th 2022

    Thanks for the alert. Could you say which section of the entry you are referring to, and/or which equation? – I have now made all equations carry a numbering.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTime5 days ago
    • (edited 5 days ago)

    In quantum mechanics, the basic notion is the von Neumann entropy defined in terms of density matrix. For type III von Neumann algebras the density matrix is not well defined (physically, the problem is usually in ultraviolet divergences). Von Neumann entropy is generalized to arbitrary semifinite von Neumann algebra in

    • I. E. Segal, A note on the concept of entropy, J. Math. Mech. 9 (1960) 623–629

    A note relating Irving Segal’s notion to relative entropy is

    (Please check)

    diff, v59, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)