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Related Concept Videos

Entropy02:39

Entropy

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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...
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Entropy01:18

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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...
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Third Law of Thermodynamics02:38

Third Law of Thermodynamics

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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.
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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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...
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Second Law of Thermodynamics02:49

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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...
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Second Law of Thermodynamics00:53

Second Law of Thermodynamics

66.4K
The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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Updated: Nov 27, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Generic Entanglement Entropy for Quantum States with Symmetry.

Yoshifumi Nakata1,2, Mio Murao3

  • 1Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

Quantum states with symmetry exhibit varying entanglement. Axial and translational symmetries maintain high entanglement, while permutation symmetry significantly reduces it, impacting quantum information science.

Keywords:
entanglement entropyrandom statessymmetry

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Physics
  • Theoretical Physics

Background:

  • Generic entanglement describes highly entangled random quantum states in Hilbert spaces.
  • This property is crucial in quantum information science and black hole physics.
  • The impact of symmetry on generic entanglement remains an open question.

Purpose of the Study:

  • To investigate how symmetries affect the generic entanglement of quantum states.
  • To analyze bipartite entanglement entropy in invariant subspaces under specific symmetries.
  • To extend concentration formulas for random states in symmetric subspaces.

Main Methods:

  • Developing a generalized concentration formula for arbitrary subspaces.
  • Analyzing quantum states drawn uniformly from invariant subspaces with axial, permutation, and translational symmetries.
  • Numerical investigation of entanglement distribution and phase transitions.

Main Results:

  • Quantum states with axial symmetry are highly entangled, but less so than generic states.
  • States with permutation symmetry exhibit significantly reduced entanglement.
  • States with translational symmetry show entanglement comparable to generic states.
  • Numerical results suggest the persistence of phase transitions in entanglement distribution.

Conclusions:

  • Symmetry plays a crucial role in modulating the entanglement properties of quantum states.
  • Different symmetries have distinct effects on entanglement, with permutation symmetry being a notable case of reduced entanglement.
  • The findings have implications for understanding quantum information processing and the fundamental nature of quantum states.