A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics
Abstract
:1. Introduction
2. Methods: Entanglement Coarse-Graining and the Surfaces of Ignorance
2.1. Macro and Microstates
2.2. Surfaces of Ignorance: Metric Components and Volume
3. Results: Volume Examples
3.1. Arbitrary N-Dimensional Unitary Transformations
3.2. Example:
3.3. Example:
3.3.1. Computing Volume
3.3.2. Analyzing the Entanglement Entropy of Macrostates
3.4. Example:
4. Generalizing the Entanglement Coarse-Graining
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
CG | Coarse-graining |
ECG | Entanglement coarse-graining |
SOI | Surfaces of ignorance |
S | System |
E | Environment |
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Ray, S.; Alsing, P.M.; Cafaro, C.; Jacinto, H.S. A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics. Entropy 2023, 25, 788. https://doi.org/10.3390/e25050788
Ray S, Alsing PM, Cafaro C, Jacinto HS. A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics. Entropy. 2023; 25(5):788. https://doi.org/10.3390/e25050788
Chicago/Turabian StyleRay, Shannon, Paul M. Alsing, Carlo Cafaro, and H S. Jacinto. 2023. "A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics" Entropy 25, no. 5: 788. https://doi.org/10.3390/e25050788
APA StyleRay, S., Alsing, P. M., Cafaro, C., & Jacinto, H. S. (2023). A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics. Entropy, 25(5), 788. https://doi.org/10.3390/e25050788