PreprintCC BY 4.0arXiv
Von Neumann's Two Quantum Entropies
Abstract
Von Neumann proposed two quantum entropies, one in 1927 and the other in 1929. He intended to define thermodynamic entropy for quantum states in both cases. The 1927 entropy is the well-known von Neumann entropy, which is zero for all pure states. The 1929 entropy, which is nonzero for almost all pure states, has largely been ignored. After reviewing the history and properties of both entropies, we argue that the 1927 entropy is not thermodynamic entropy and should be used simply as a measure of entanglement, whereas the 1929 entropy is the true thermodynamic entropy for quantum states.
Related
- Sharp Data-Processing Region for Quantum Conditional Rényi Entropies
- Improved Quantum Algorithms for Rényi Entropies Estimation
- Quantum channels on duals of von Neumann algebras in the Schrödinger picture
- Harnessing Post-selected von Neumann Measurements to Strengthen Entanglement and Quantum Signatures in Coherent States
- A Generalized quantum Stein lemma on von Neumann algebras
BibTeX
@misc{wu2026neumanns,
title = {{Von Neumann's Two Quantum Entropies}},
author = {Biao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30284},
eprint = {2609.30284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30284},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Von Neumann's Two Quantum Entropies
AU - Biao Wu
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.30284
UR - https://arxiv.org/abs/2609.30284
AB - Von Neumann proposed two quantum entropies, one in 1927 and the other in 1929. He intended to define thermodynamic entropy for quantum states in both cases. The 1927 entropy is the well-known von Neumann entropy, which is zero for all pure states. The 1929 entropy, which is nonzero for almost all pure states, has largely been ignored. After reviewing the history and properties of both entropies, we argue that the 1927 entropy is not thermodynamic entropy and should be used simply as a measure of entanglement, whereas the 1929 entropy is the true thermodynamic entropy for quantum states.
ER -