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

Entropy02:39

Entropy

34.6K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
34.6K
Entropy01:18

Entropy

3.4K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.4K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

21.4K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
21.4K
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

2.2K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
2.2K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

4.6K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
4.6K
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

26.5K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
26.5K

You might also read

Related Articles

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

Sort by
Same author

Eigenstate Thermalization Hypothesis Correlations via Nonlinear Hydrodynamics.

Physical review letters·2026
Same author

Emergence of Generic Entanglement Structure in Doped Matchgate Circuits.

Physical review letters·2026
Same author

Information geometry of transitions between quantum nonequilibrium steady states.

Physical review. E·2025
Same author

Enhancing Revivals via Projective Measurements in a Quantum Scarred System.

Physical review letters·2025
Same author

Multipartite Entanglement Structure of Monitored Quantum Circuits.

Physical review letters·2025
Same author

Quantum stochastic thermodynamics in the mesoscopic-leads formulation.

Physical review. E·2025
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Dec 28, 2025

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

8.9K

Multipartite Entanglement Structure in the Eigenstate Thermalization Hypothesis.

Marlon Brenes1, Silvia Pappalardi2,3, John Goold1

  • 1Department of Physics, Trinity College Dublin, Dublin 2, Ireland.

Physical Review Letters
|February 15, 2020
PubMed
Summary
This summary is machine-generated.

We explored quantum Fisher information (QFI) in thermal pure states under the eigenstate thermalization hypothesis (ETH). Our findings reveal distinct entanglement structures compared to canonical ensembles, even when local observables appear similar.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K
Submillisecond Conformational Changes in Proteins Resolved by Photothermal Beam Deflection
10:02

Submillisecond Conformational Changes in Proteins Resolved by Photothermal Beam Deflection

Published on: February 18, 2014

9.3K

Related Experiment Videos

Last Updated: Dec 28, 2025

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

8.9K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.9K
Submillisecond Conformational Changes in Proteins Resolved by Photothermal Beam Deflection
10:02

Submillisecond Conformational Changes in Proteins Resolved by Photothermal Beam Deflection

Published on: February 18, 2014

9.3K

Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • The eigenstate thermalization hypothesis (ETH) describes how isolated quantum systems reach thermal equilibrium.
  • Understanding multipartite entanglement in thermal states is crucial for quantum many-body physics.
  • Quantum Fisher Information (QFI) quantifies the ultimate precision in estimating quantum states.

Purpose of the Study:

  • To investigate the quantum Fisher information (QFI) and multipartite entanglement structure of thermal pure states within the framework of the eigenstate thermalization hypothesis (ETH).
  • To compare the entanglement properties derived from ETH with those of the canonical ensemble.
  • To provide a numerical example demonstrating extensive QFI in a quantum many-body system under ETH.

Main Methods:

  • Explicit calculation of QFI from response functions in both canonical and ETH contexts.
  • Theoretical analysis of the relationship between QFI in ETH and canonical ensembles.
  • Numerical simulation of a quantum many-body system to illustrate differences in QFI.

Main Results:

  • The QFI expression derived from ETH provides an upper bound for the corresponding canonical ensemble expression.
  • Despite indistinguishable average values and fluctuations of local observables, the entanglement structures differ significantly between ETH and canonical ensembles.
  • A numerical example demonstrates extensive QFI in a quantum many-body system under ETH, while the canonical ensemble QFI vanishes.

Conclusions:

  • The entanglement structure of thermal pure states under ETH is fundamentally different from canonical ensembles, with implications for quantum phase transitions.
  • These findings are relevant for understanding entanglement in the long-time evolution of quenched quantum many-body systems.
  • The study highlights the power of QFI as a sensitive probe of multipartite entanglement in quantum systems beyond equilibrium thermodynamics.