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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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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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Consider an infinitesimal step in the expansion, which...
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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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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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The Second Law of Thermodynamics01:14

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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. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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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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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Entropy of Quantum States.

Paolo Facchi1,2, Giovanni Gramegna3, Arturo Konderak1,2

  • 1Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy.

Entropy (Basel, Switzerland)
|June 2, 2021
PubMed
Summary

We introduce a novel algebraic definition for entropy in quantum systems, resolving ambiguities in state representation and von Neumann entropy calculations. This new entropy satisfies thermodynamic properties and aligns with quantum mechanical principles.

Keywords:
operator algebraquantum entropyquantum statistical mechanics

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Area of Science:

  • Quantum Information Theory
  • Mathematical Physics
  • Statistical Mechanics

Background:

  • Quantum systems can be described by algebras of observables.
  • Selection rules can lead to multiple density matrices representing a single quantum state.
  • This ambiguity results in different von Neumann entropies for the same state.

Purpose of the Study:

  • To resolve the ambiguity in entropy definition for quantum states.
  • To introduce a purely algebraic definition of entropy.
  • To ensure the new entropy definition satisfies thermodynamic properties.

Main Methods:

  • Developed a purely algebraic definition of entropy for states of an algebra of observables.
  • Utilized the minimality property of von Neumann entropy concerning decompositions into pure states.
  • Demonstrated the equivalence to von Neumann entropy in specific quantum mechanical representations.

Main Results:

  • A unique algebraic entropy definition is established for quantum states.
  • The defined entropy aligns with desirable thermodynamic properties.
  • The algebraic entropy equals the von Neumann entropy for multiplicity-free representations.

Conclusions:

  • The proposed algebraic entropy definition successfully resolves ambiguities in quantum state entropy.
  • This framework provides a robust and consistent approach to quantum entropy.
  • The findings have implications for understanding quantum information and thermodynamics.