In quantum statistical mechanics, von Neumann entropy, named after John von Neumann, is the extension of classical entropy concepts to the field of quantum mechanics. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is
where tr denotes the trace. If ρ is written in terms of its eigenvectors |1〉, |2〉, |3〉, ... as
then the von Neumann entropy is
In this form, S can be seen to be related to the Shannon entropy.
Read more about Von Neumann Entropy: Background, Definition, Properties, Uses
Famous quotes containing the words von, neumann and/or entropy:
“The new vulcanism is really a daring attempt to connect the present, incomprehensible world to a past, unknown one.”
—Johann Wolfgang Von Goethe (17491832)
“It means there are times when a mere scientist has gone as far as he can. When he must pause and observe respectfully while something infinitely greater assumes control.”
—Kurt Neumann (19061958)
“Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.”
—Václav Havel (b. 1936)