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Von Neumann entropy - Wikipedia
In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is 展开
John von Neumann established a rigorous mathematical framework for quantum mechanics in his 1932 work Mathematical Foundations of Quantum Mechanics. In it, he provided a theory of … 展开
Some properties of the von Neumann entropy:
• S(ρ) is zero if and only if ρ represents a pure state.
• S(ρ) is … 展开Given the density matrix ρ, von Neumann defined the entropy as
$${\displaystyle S(\rho )=-\operatorname {tr} (\rho \ln \rho ),}$$
which is a proper … 展开Since, for a pure state, the density matrix is idempotent, ρ = ρ , the entropy S(ρ) for it vanishes. Thus, if the system is finite (finite-dimensional matrix … 展开
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