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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...
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...

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Related Experiment Video

Updated: May 30, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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

Published on: December 4, 2017

Energy dissipation via coupling with a finite chaotic environment.

M A Marchiori1, M A M de Aguiar

  • 1Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas, SP, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary

Energy dissipation and thermalization occur in chaotic systems with nonlinear oscillators. This study shows that a harmonic oscillator coupled to a chaotic environment reaches a Boltzmann energy distribution, validated by linear response theory.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: March 5, 2011

Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Quantum Chaos

Background:

  • Understanding energy flow between quantum systems and their environments is crucial for quantum technologies.
  • Nonlinear oscillators provide a rich platform for studying complex dynamics and thermalization.
  • The transition from integrable to chaotic behavior in a system influences its thermodynamic properties.

Purpose of the Study:

  • To investigate energy dissipation and thermalization of a harmonic oscillator coupled to a nonlinear environment.
  • To determine the conditions (system size N, dynamical regime) for energy flow and thermalization.
  • To develop an analytical model explaining the observed phenomena.

Main Methods:

  • Classical molecular dynamics simulations of a harmonic oscillator coupled to N nonlinear oscillators.
  • Analysis of energy flow and distribution as a function of N and oscillator dynamics.
  • Application of linear response theory for analytical validation.

Main Results:

  • Dissipation and thermalization are observed in the chaotic regime for small N.
  • The harmonic oscillator and environment reach a Boltzmann distribution at a defined temperature.
  • Analytical treatment based on linear response theory successfully reproduces simulation results for chaotic environments.

Conclusions:

  • Chaotic nonlinear environments facilitate efficient energy dissipation and thermalization of coupled harmonic oscillators.
  • The system's dynamical regime (chaotic vs. integrable) is critical for thermalization.
  • Linear response theory provides a valid framework for understanding energy transfer in such systems.