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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...
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

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...
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...
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...
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Dynamical thermalization of disordered nonlinear lattices.

Mario Mulansky1, Karsten Ahnert, Arkady Pikovsky

  • 1Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Strasse 24, D-14476 Potsdam-Golm, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

Energy spreads in disordered nonlinear lattices, leading to dynamical thermalization. A growing fraction of modes thermalize as nonlinearity increases, showing an ergodic chaotic state.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Nonlinear dynamics

Background:

  • Disordered systems often exhibit Anderson localization, preventing energy spread.
  • Nonlinearity can potentially overcome localization, but its effect on thermalization is complex.

Purpose of the Study:

  • To numerically investigate energy spreading in a finite disordered nonlinear lattice.
  • To establish the emergence and characteristics of dynamical thermalization in such systems.

Main Methods:

  • Numerical simulations of energy dynamics on a one-dimensional lattice.
  • Analysis of mode localization and the emergence of chaotic states.

Main Results:

  • All linear modes are exponentially localized by disorder.
  • Dynamical thermalization emerges, characterized by an ergodic chaotic state.
  • A finite fraction of modes thermalize, increasing with nonlinearity strength.

Conclusions:

  • Nonlinearity can drive thermalization even in the presence of strong disorder.
  • The degree of thermalization is tunable via nonlinearity strength.