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Von neumann entropy, log(P) ?

  1. Mar 29, 2005 #1
    Let P be a density matrix. Then the von neumann entropy is defined as
    S(P) = -tr(P*log(P))

    But how is log(P) defined ?

    found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.
    Last edited: Mar 29, 2005
  2. jcsd
  3. Mar 29, 2005 #2
    [tex]ln(P) = -\sum_{n=1}^\infty \frac{1}{n}(I-A)^n[/tex]
  4. Mar 29, 2005 #3
    right. Usually easier by the way !
  5. Mar 29, 2005 #4


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    The definition is really

    [tex] S:=-k\langle \ln\hat{\rho}\rangle_{\hat{\rho}} [/tex]

    ,quite similar to Gibbs' entropy.

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