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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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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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Entropy and the Second Law of Thermodynamics01:26

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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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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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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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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Average diagonal entropy in nonequilibrium isolated quantum systems.

Olivier Giraud1, Ignacio García-Mata2,3

  • 1LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.

Physical Review. E
|August 31, 2016
PubMed
Summary
This summary is machine-generated.

We analytically calculated the average diagonal entropy for isolated quantum systems subjected to cyclic quenches. Our findings validate recent heuristic relations and offer insights into non-equilibrium quantum dynamics.

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Diagonal entropy is a promising measure for characterizing isolated quantum systems, particularly those out of equilibrium.
  • Understanding entropy in non-equilibrium quantum dynamics is crucial for fundamental physics and potential applications.

Purpose of the Study:

  • To analytically compute the average diagonal entropy for quantum systems under unitary evolution with cyclic quenches.
  • To compare analytical results with numerical simulations for validation.
  • To clarify and elucidate recently proposed heuristic relations in the literature.

Main Methods:

  • Analytical calculation of average diagonal entropy.
  • Modeling quantum systems undergoing unitary evolution and cyclic quenches.
  • Numerical simulations of various quantum systems for comparison.

Main Results:

  • The analytical calculations provide a precise method for determining average diagonal entropy in perturbed quantum systems.
  • Agreement between analytical predictions and numerical simulations confirms the validity of the approach.
  • The study clarifies the theoretical underpinnings of heuristic relations concerning diagonal entropy.

Conclusions:

  • The analytical framework presented is effective for studying non-equilibrium dynamics in isolated quantum systems.
  • The work provides a rigorous foundation for understanding diagonal entropy and its behavior under perturbations.
  • This research contributes to the theoretical toolkit for analyzing quantum information in complex quantum systems.