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Related Concept Videos

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...
Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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...

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Related Experiment Video

Updated: May 29, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Orthogonality of two-dimensional separations based on conditional entropy.

Mohammad Reza Pourhaghighi1, Mohammad Karzand, Hubert H Girault

  • 1Laboratoire d'Electrochimie Physique et Analytique, Station 6, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland.

Analytical Chemistry
|September 15, 2011
PubMed
Summary

A novel method using conditional entropy quantifies the orthogonality of two-dimensional (2-D) separation systems. This approach is independent of peak numbers, enabling direct comparison of different separation techniques for samples like peptides.

Related Experiment Videos

Last Updated: May 29, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

  • Analytical Chemistry
  • Separation Science
  • Biochemistry

Background:

  • Two-dimensional (2-D) separation techniques are crucial for complex sample analysis.
  • Assessing the orthogonality of these systems is vital for maximizing separation power.
  • Existing orthogonality measures can be dependent on the number of detected peaks.

Purpose of the Study:

  • To develop a new, robust method for assessing the orthogonality of 2-D separation systems.
  • To create a quantitative measure of orthogonality that is independent of peak count.
  • To enable direct comparison of different 2-D separation protocols.

Main Methods:

  • A novel approach based on conditional entropy was developed to quantify orthogonality.
  • The method considers the quantitative distribution of peaks across the entire separation space.
  • The developed method was applied to estimate the orthogonality of off-gel electrophoresis (OGE) coupled with capillary zone electrophoresis (CZE) for peptide separation.

Main Results:

  • The developed conditional entropy-based method provides an orthogonality measure independent of the number of observed peaks.
  • This allows for a more objective comparison of different 2-D separation systems.
  • The orthogonality of OGE-CZE for peptide separation was successfully estimated using this new approach.

Conclusions:

  • Conditional entropy offers a reliable metric for evaluating 2-D separation system orthogonality.
  • The developed method provides a universally applicable tool for comparing diverse separation strategies.
  • This advancement facilitates the optimization of 2-D separation protocols in analytical chemistry.