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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 Thermodynamics01:20

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...
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...

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Related Experiment Video

Updated: Jul 13, 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

Quantum mechanical heat transport in disordered harmonic chains.

Christopher Gaul1, Helmut Büttner

  • 1Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany. christopher.gaul@uni-bayreuth.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
Summary

This study explores heat conduction in one-dimensional chains using quantum Langevin methods. Disordered chains show normal heat conduction with quantum effects, while ordered chains exhibit classical behavior.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • Understanding heat conduction mechanisms is crucial in condensed matter physics.
  • Quantum effects can significantly alter thermal transport properties in low-dimensional systems.
  • Distinguishing between normal and anomalous heat conduction requires careful analysis of temperature gradients and system length dependence.

Purpose of the Study:

  • To investigate the mechanism of heat conduction in one-dimensional harmonic chains.
  • To analyze the differences in thermal transport between ordered and disordered chains.
  • To identify and characterize quantum mechanical features influencing heat conduction.

Main Methods:

  • Utilized the quantum mechanical Langevin method for simulations.
  • Studied both ordered and disordered harmonic one-dimensional chains.
  • Analyzed temperature gradients, heat flux, and mode occupation statistics.

Main Results:

  • Disordered chains exhibit indications of normal heat conduction, with a finite temperature gradient.
  • Observed quantum phenomena including Bose-Einstein statistics, freezing of heat conductivity, and entanglement effects.
  • Ordered chains reproduce classical results: vanishing temperature gradient and length-independent heat flux.

Conclusions:

  • Quantum mechanics introduces unique features to heat conduction in disordered chains.
  • The behavior of heat conduction in disordered chains suggests normal transport, but length dependence requires further investigation.
  • Ordered chains behave classically, confirming established theoretical predictions.