Von Neumann entropy

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In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system. It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics, and it is the quantum counterpart of the Shannon entropy from classical information theory. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is S = − tr ⁡ ( ρ ln ⁡ ρ ) , {\displaystyle S=-\operatorname {tr} (\rho \ln \rho ),} where tr {\displaystyle \operatorname {tr} } denotes the trace and ln {\displaystyle \operatorname {ln} } denotes the matrix version of the natural logarithm. If the density matrix ρ is written in a basis of its eigenvectors...

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