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

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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.
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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...
Entropy02:39

Entropy

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...
Entropy01:18

Entropy

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...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...

You might also read

Related Articles

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

Sort by
Same author

Large Scale Quantum Chemistry with Tensor Processing Units.

Journal of chemical theory and computation·2022
Same author

Large-scale distributed linear algebra with tensor processing units.

Proceedings of the National Academy of Sciences of the United States of America·2022
Same author

Conformal Fields and Operator Product Expansion in Critical Quantum Spin Chains.

Physical review letters·2020
Same author

Conformal Data and Renormalization Group Flow in Critical Quantum Spin Chains Using Periodic Uniform Matrix Product States.

Physical review letters·2018
Same author

Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm.

Physical review letters·2017
Same author

First order phase transition in the anisotropic quantum orbital compass model.

Physical review letters·2009

Related Experiment Video

Updated: Jul 6, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Entanglement renormalization and topological order.

Miguel Aguado1, Guifré Vidal

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1. D-85748 Garching, Germany.

Physical Review Letters
|March 21, 2008
PubMed
Summary
This summary is machine-generated.

The multiscale entanglement renormalization ansatz (MERA) offers a natural description for topological states of matter. This tensor network approach simplifies Kitaev

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

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

Related Experiment Videos

Last Updated: Jul 6, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

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

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

Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Quantum Matter

Background:

  • Topological states of matter exhibit unique properties robust against local perturbations.
  • The multiscale entanglement renormalization ansatz (MERA) is a powerful tensor network framework for studying quantum many-body systems.
  • Understanding the MERA description of topological phases is crucial for developing fault-tolerant quantum computation.

Purpose of the Study:

  • To investigate the suitability of the multiscale entanglement renormalization ansatz (MERA) for describing topological states of matter.
  • To analyze the MERA representation of Kitaev's toric code and its implications for topological degrees of freedom.
  • To explore the generalization of these findings to broader classes of topological models.

Main Methods:

  • Applying the multiscale entanglement renormalization ansatz (MERA) to analyze topological states.
  • Detailed analysis of Kitaev's toric code within the MERA framework.
  • Investigating renormalization group flow for entanglement renormalization fixed points.
  • Generalizing the MERA description to quantum double models.

Main Results:

  • The multiscale entanglement renormalization ansatz (MERA) provides a natural and simplified description for topological states.
  • Kitaev's toric code exhibits a remarkably simple MERA structure, distilling topological degrees of freedom.
  • Kitaev states on infinite lattices are identified as fixed points of the entanglement renormalization group flow.
  • The developed MERA framework is shown to generalize to arbitrary quantum double models.

Conclusions:

  • The multiscale entanglement renormalization ansatz (MERA) is a suitable and effective tool for characterizing topological states of matter.
  • MERA offers a pathway to understanding and manipulating topological degrees of freedom in quantum systems.
  • The results pave the way for applying MERA to a wider range of topological quantum phases and related phenomena.