Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

3.7K
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
3.7K
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

3.1K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
3.1K
Divergence and Curl01:15

Divergence and Curl

2.9K
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...
2.9K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.0K
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

6.7K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
6.7K
The Uncertainty Principle04:08

The Uncertainty Principle

30.2K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
30.2K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Evaluation of commercial susceptibility testing methods for <i>in vitro</i> determining daptomycin susceptibility in vancomycin-resistant <i>Enterococcus faecium</i>.

Microbiology spectrum·2026
Same author

Surgeon seniority and performance in breast-conserving surgery for non-palpable lesions: evidence from a multicenter study.

Breast (Edinburgh, Scotland)·2026
Same author

Comparative effectiveness of preoperative localization techniques for non-palpable breast lesions: multicentre real-world study.

BJS open·2026
Same author

Performance of disc diffusion and gradient strip test on different Mueller-Hinton agar media plates and ComASP® and Bruker UMIC® Cefiderocol Microdilution Panels for cefiderocol susceptibility testing in carbapenem-resistant Pseudomonas aeruginosa.

The Journal of antimicrobial chemotherapy·2025
Same author

Overestimation of piperacillin/tazobactam resistance in Escherichia coli by disc diffusion and gradient strip methods.

The Journal of antimicrobial chemotherapy·2025
Same author

A European survey on anaerobes from paediatric blood cultures: a comparative analysis with adults.

European journal of clinical microbiology & infectious diseases : official publication of the European Society of Clinical Microbiology·2025
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Nov 27, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

952

Canonical Divergence for Measuring Classical and Quantum Complexity.

Domenico Felice1, Stefano Mancini2,3, Nihat Ay1,4,5

  • 1Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

A novel canonical divergence unifies complexity measures for classical and quantum systems. This information-geometric tool generalizes Kullback-Leibler divergence and quantum relative entropy, offering a unified approach to system complexity.

Keywords:
differential geometryquantum informationriemannian geometries

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.0K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.8K

Related Experiment Videos

Last Updated: Nov 27, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

952
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.0K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.8K

Area of Science:

  • Information Geometry
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Existing measures of complexity in classical and quantum systems lack a unified framework.
  • Kullback-Leibler divergence is a standard measure for classical probability distributions.
  • Quantum relative entropy quantifies differences between quantum states.

Purpose of the Study:

  • To introduce a new canonical divergence for generalizing information-geometric complexity measures.
  • To demonstrate the unified applicability of this divergence across classical and quantum systems.
  • To establish connections between classical and quantum information-geometric concepts.

Main Methods:

  • Development of a novel canonical divergence based on information-geometric principles.
  • Mathematical proofs demonstrating the divergence's behavior on the simplex of probability measures.
  • Mathematical proofs showing the divergence's reduction to quantum relative entropy on the space of positive density operators.

Main Results:

  • The new canonical divergence coincides with Kullback-Leibler divergence for classical probability measures.
  • The divergence reduces to quantum relative entropy for quantum density operators.
  • This establishes a unified information-geometric measure of complexity.

Conclusions:

  • The proposed canonical divergence provides a generalized framework for quantifying complexity in both classical and quantum systems.
  • It bridges the gap between classical information theory (Kullback-Leibler divergence) and quantum information theory (quantum relative entropy).
  • This unified measure has potential applications in diverse fields, including statistical mechanics and machine learning.