General properties of entropy
Abstract
It is rather paradoxical that, although entropy is one of the most important quantities in physics, its main properties are rarely listed in the usual textbooks on statistical mechanics. In this paper we try to fill this gap by discussing these properties, as, for instance, invariance, additivity, concavity, subadditivity, strong subadditivity, continuity, etc., in detail, with reference to their implications in statistical mechanics. In addition, we consider related concepts such as relative entropy, skew entropy, dynamical entropy, etc. Taking into account that statistical mechanics deals with large, essentially infinite systems, we finally will get a glimpse of systems with infinitely many degrees of freedom.
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When von Neumann entropy approaches 1, latent variables cannot predict the density matrix values.
“When von Neumann entropy approaches 1, it indicates that latent variables cannot predict the density matrix values.”
From Mathematical proof of the Fisher-Escolà <i>Q</i> statistical distribution in quantum consciousness modeling (2025) · cites this paper as [72]
In pure entanglement, entropy near zero ensures that entanglement alone determines the qubit states.
“in pure entanglement, entropy should be near zero, ensuring that entanglement alone determines the qubit states.”
From Mathematical proof of the Fisher-Escolà <i>Q</i> statistical distribution in quantum consciousness modeling (2025) · cites this paper as [72]
Low von Neumann entropy (close to 0) indicates pure entangled states.
“To ensure pure entangled states, the entropy of the density matrix should ideally be low or close to 0.”
From Mathematical proof of the Fisher-Escolà <i>Q</i> statistical distribution in quantum consciousness modeling (2025) · cites this paper as [72]
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- Authors
- Wehrl, A.
- Affiliations
- University of Vienna (AT)
- Corresponding author
- Wehrl, Alfred
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1978-04-01
- Volume
- 50
- Issue
- 2
- Pages
- 221-260
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2055281720
- Semantic Scholar
- 15107bdf4f5c8daf55e4d66e14971088ee19843d
- Cited by
- 1,963
- References
- 121
- Citations by year
- 2026: 44 · 2025: 71 · 2024: 100 · 2023: 112 · 2022: 59 · 2021: 73 · 2020: 71 · 2019: 59 · 2018: 62 · 2017: 50 · 2016: 64 · 2015: 51 · 2014: 56 · 2013: 56 · 2012: 44
- FWCI
- 13.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reviews of Modern Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- entropy, additivity, concavity, subadditivity, strong subadditivity, Kullback-Leibler divergence, dynamical entropy, infinite systems, statistical mechanics
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