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Related Concept Videos

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

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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.
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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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The Entropy as a State Function01:14

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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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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.
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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...

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Entanglement entropy and the Fermi surface.

Brian Swingle1

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. bswingle@mit.edu

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Free fermions with finite Fermi surfaces show unusually high entanglement entropy, scaling as L(d-1)logL. This work explains this anomaly using a low-energy model, predicting similar boundary law violations in other correlated systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory

Background:

  • Free fermions with finite Fermi surfaces exhibit anomalous entanglement entropy.
  • The standard boundary law for entanglement entropy is S∼L(d-1).

Purpose of the Study:

  • To provide an intuitive explanation for the anomalous entanglement entropy scaling in free fermions.
  • To predict boundary law violations in other strongly correlated systems.

Main Methods:

  • Analysis of entanglement entropy in free fermion systems.
  • Low-energy description of Fermi surfaces as 1D gapless modes.

Main Results:

  • The leading entanglement entropy contribution scales as S∼L(d-1)logL, deviating from the usual boundary law.
  • This anomalous scaling depends on Fermi surface geometry and region boundary.

Conclusions:

  • An intuitive explanation for anomalous entanglement entropy is provided via a 1D gapless mode picture.
  • Boundary law violations are predicted for other strongly correlated systems.