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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

Entropy

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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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Entropy and the Second Law of Thermodynamics01:20

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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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Third Law of Thermodynamics02:38

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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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Second Law of Thermodynamics02:49

Second Law of Thermodynamics

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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

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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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Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases.

Maximilian Kiefer-Emmanouilidis1,2, Razmik Unanyan1, Michael Fleischhauer1

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In disordered quantum systems, number entropy (S_N) grows logarithmically over time (lnlnt), suggesting slow particle transport even in localized states. This behavior aligns with theories linking entanglement and number entropy.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Disordered quantum systems exhibit complex behaviors like many-body localization.
  • Particle number fluctuations are crucial for understanding transport properties.

Purpose of the Study:

  • Investigate number entropy (S_N) dynamics after a quantum quench in 1D disordered systems.
  • Characterize particle transport in the many-body localization regime.

Main Methods:

  • Analysis of number entropy (S_N) growth.
  • Comparison with entanglement entropy (S) scaling.
  • Theoretical framework for disordered interacting systems.

Main Results:

  • Number entropy exhibits a subdiffusive growth of S_N∼lnlnt.
  • This slow transport persists in the many-body localization regime.
  • Observed growth is consistent with established entanglement-number entropy relations.

Conclusions:

  • Number entropy provides insights into subdiffusive transport in localized quantum systems.
  • The findings support theoretical connections between different entropy measures.