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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

Entropy

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...
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

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...
Second Law of Thermodynamics00:53

Second Law of Thermodynamics

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 chemical energy...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Quantum chaos and effective thermalization.

Alexander Altland1, Fritz Haake

  • 1Institut für Theoretische Physik, Universität zu Köln, Köln, Germany.

Physical Review Letters
|March 10, 2012
PubMed
Summary
This summary is machine-generated.

We show how quantum systems reach thermal equilibrium even with classical chaos. Using the Dicke model, we found a "quantum smoothened" path to equilibrium, avoiding classical singularities.

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Area of Science:

  • Quantum Dynamics
  • Statistical Mechanics
  • Quantum Chaos

Background:

  • Unitary quantum dynamics can exhibit thermalization under classical chaos.
  • The Dicke model serves as a key example for studying quantum-classical transitions.

Purpose of the Study:

  • To demonstrate effective equilibration for unitary quantum dynamics in classically chaotic systems.
  • To provide a constructive description of thermalization using phase-space distributions.

Main Methods:

  • Focusing on the Dicke model, a paradigmatic system.
  • Utilizing the Glauber Q or Husimi function to describe the quantum state.
  • Deriving and analyzing a Fokker-Planck type evolution equation.

Main Results:

  • The evolution equation reveals a balance between classical drift and quantum diffusion.
  • A "quantum smoothened" approach to equilibrium is observed.
  • This mechanism circumvents singularities typical of classical chaotic flows.

Conclusions:

  • Effective thermalization is achievable in unitary quantum dynamics under classical chaos.
  • Phase-space distributions offer a powerful tool for understanding quantum thermalization.
  • The Fokker-Planck description captures the essential dynamics of quantum smoothening towards equilibrium.