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Related Concept Videos

The Thermodynamics of Mixing01:28

The Thermodynamics of Mixing

Mixing is a fascinating phenomenon in thermodynamics, particularly when considering the Gibbs energy of a mixture at constant temperature and pressure. This energy, denoted as G, tends to decrease during spontaneous mixing processes, offering insights into the composition changes that occur.Imagine two ideal gases, initially separated in different containers, with amounts nA and nB, respectively, both at a temperature T and pressure p. The chemical potentials of these gases have their 'pure'...
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 Solvation02:05

Entropy and Solvation

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an...
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
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 10, 2026

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
10:12

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Published on: June 12, 2015

Quantifying disorder through conditional entropy: an application to fluid mixing.

Giovanni B Brandani1, Marieke Schor, Cait E Macphee

  • 1SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, Scotland, United Kingdom.

Plos One
|June 14, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method using conditional entropies to quantify system disorder, outperforming traditional measures in fluid membranes. The approach accurately captures local correlations and reduces binning dependence for diverse applications.

More Related Videos

Quantifying Mixing using Magnetic Resonance Imaging
07:33

Quantifying Mixing using Magnetic Resonance Imaging

Published on: January 25, 2012

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Last Updated: May 10, 2026

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
10:12

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

Published on: June 12, 2015

Quantifying Mixing using Magnetic Resonance Imaging
07:33

Quantifying Mixing using Magnetic Resonance Imaging

Published on: January 25, 2012

Area of Science:

  • Statistical mechanics
  • Physical chemistry
  • Materials science

Background:

  • Quantifying disorder is crucial in various scientific fields.
  • Existing global measures of disorder have limitations, especially in complex systems.
  • Local correlations and fine-grained disorder are often overlooked by mean-field approaches.

Purpose of the Study:

  • To develop a robust method for quantifying system disorder.
  • To address limitations of existing disorder measures, particularly their dependence on binning and inability to capture local correlations.
  • To provide a versatile tool applicable to both continuum and lattice models.

Main Methods:

  • Utilizing conditional entropies as a measure of disorder.
  • Applying the method to analyze mixing and demixing phenomena in multicomponent fluid membranes.
  • Comparing the efficacy of conditional entropies against traditional Shannon entropy-based measures.

Main Results:

  • The conditional entropy method effectively quantifies disorder, even when global measures fail.
  • Demonstrated reduced dependence on binning compared to Shannon entropy measures.
  • Successfully captured local correlations in fluid membrane systems.
  • The method is rigorous for lattice models and applicable to continuum models.

Conclusions:

  • Conditional entropies offer a superior approach to quantifying disorder, especially for capturing local correlations.
  • The developed method presents significant advantages over existing techniques for analyzing complex systems.
  • Potential applications span fluid mixtures, liquid crystals, magnetic materials, and biomolecular systems, highlighting its broad utility.