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Related Concept Videos

Diffusion01:12

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
Transition State Theory01:25

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Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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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.
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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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Related Experiment Video

Updated: Jun 25, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Entropy rate of diffusion processes on complex networks.

Jesús Gómez-Gardeñes1, Vito Latora

  • 1Scuola Superiore di Catania, Via S. Nullo 5/i, 95123 Catania, Italy. jesus.gardenes@ct.infn.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

We introduce entropy rate to analyze diffusion on complex networks. This measure reveals network topology and dynamics, guiding optimal diffusion process design for various systems.

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Area of Science:

  • Network Science
  • Information Theory
  • Complex Systems

Background:

  • Diffusion processes are fundamental to understanding complex networks.
  • Characterizing network topology and dynamics is crucial for system analysis.
  • Existing methods may not fully capture the nuances of diffusion on intricate structures.

Purpose of the Study:

  • To introduce and define the concept of entropy rate for diffusion processes on complex networks.
  • To demonstrate the sensitivity of entropy rate to network topology and dynamics.
  • To explore the application of entropy rate in designing optimal diffusion processes.

Main Methods:

  • Development of the entropy rate concept for network diffusion.
  • Analysis of entropy rate's sensitivity to network structural properties.
  • Investigation of entropy maximization principles for process optimization.

Main Results:

  • Entropy rate quantifies the minimal information needed to describe network diffusion.
  • Entropy rate is highly sensitive to complex network topology and dynamics.
  • Entropy maximization provides a framework for designing efficient diffusion strategies.

Conclusions:

  • Entropy rate offers a novel theoretical tool for network analysis.
  • The findings have potential applications in social, technological, and communication systems.
  • This work advances the understanding of information flow and process design in complex networks.