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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 Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Ziegler–Natta Chain-Growth Polymerization: Overview01:17

Ziegler–Natta Chain-Growth Polymerization: Overview

Ziegler–Natta polymerization is another form of addition or chain‐growth polymerization used for synthesizing linear polymers over branched polymers. The catalyst used for polymerization is the Ziegler–Natta catalyst, named after Karl Ziegler and Giulio Natta, who developed it in 1953. This catalyst is an organometallic complex of titanium tetrachloride and triethyl aluminum, with the active form of the catalyst being an alkyl titanium compound. Using the Ziegler–Natta catalyst, high molecular...
Intrinsically Disordered Proteins02:18

Intrinsically Disordered Proteins

Intrinsically disordered proteins are a group of proteins that do not fold into specific three-dimensional structures. Their structural flexibility allows them to complement ordered proteins to perform functions that are inaccessible to rigid structures. They are more common in eukaryotes than prokaryotes and may either be exclusively intrinsically disordered or hybrid proteins, consisting of a mix of ordered and disordered regions. The absence of a rigid structure in these proteins can be...
Intrinsically Disordered Proteins02:18

Intrinsically Disordered Proteins

Intrinsically disordered proteins are a group of proteins that do not fold into specific three-dimensional structures. Their structural flexibility allows them to complement ordered proteins to perform functions that are inaccessible to rigid structures. They are more common in eukaryotes than prokaryotes and may either be exclusively intrinsically disordered or hybrid proteins, consisting of a mix of ordered and disordered regions. The absence of a rigid structure in these proteins can be...

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Updated: May 30, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Thermalization of strongly disordered nonlinear chains.

Tsampikos Kottos1, Boris Shapiro

  • 1Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary
This summary is machine-generated.

Correlated disorder potentials significantly accelerate thermalization in discrete nonlinear Schrödinger systems. This leads to a standard grand canonical distribution, even with fixed effective disorder strength.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Condensed matter theory

Background:

  • The discrete nonlinear Schrödinger equation (DNLSE) models various physical systems, including nonlinear optics and Bose-Einstein condensates.
  • Understanding thermalization in disordered systems is crucial for predicting their long-term behavior.
  • Strong disorder typically leads to Anderson localization, hindering thermalization.

Purpose of the Study:

  • To investigate the impact of disorder correlations on the thermalization of DNLSE systems.
  • To determine if correlated disorder can facilitate thermalization in the strong disorder limit.
  • To analyze the resulting probability distribution of site norms.

Main Methods:

  • Theoretical analysis of the DNLSE with correlated disorder potentials.
  • Numerical simulations of wave-packet dynamics in disordered DNLSE systems.
  • Characterization of thermalization via the distribution of probability norms.

Main Results:

  • Introducing correlations in the disorder potential significantly enhances the thermalization rate.
  • This facilitation occurs even when the effective disorder strength, measured by localization properties, remains constant.
  • The system achieves a standard grand canonical distribution of probability norms across sites.

Conclusions:

  • Disorder correlations play a critical role in the thermalization dynamics of DNLSE systems.
  • Correlated disorder offers a pathway to overcome localization effects and achieve thermal equilibrium.
  • The findings have implications for controlling and predicting the behavior of complex nonlinear systems.