Quantum mechanical entropy

Von Neumann entropy

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 where denotes the trace and ln denotes the (natural) matrix logarithm. If ρ is written in terms of its eigenvectors as then the von Neumann entropy is merely In this form, S can be seen as the information theoretic Shannon entropy. The von Neumann entropy is also used in different forms (conditional entropies, relative entropies, etc.) in the framework of quantum information theory to characterize the entropy of entanglement. (Wikipedia).

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From playlist Natural Sciences

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From playlist Mathematics

Related pages

Entropy of entanglement | Trace (linear algebra) | Quantum statistical mechanics | Entropy (statistical thermodynamics) | Hermitian matrix | Density matrix | Bell state | Wehrl entropy | Logarithm of a matrix | Majorization | Information theory | John von Neumann | Idempotent matrix | Probability distribution | Quantum entanglement | Partition function (statistical mechanics) | Quantum mutual information | Hilbert space | Subadditivity | Conditional entropy | Partition function (mathematics) | Entropy (information theory) | Eigendecomposition of a matrix | Triangle inequality