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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...
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
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...
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...
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.

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Related Experiment Video

Updated: May 28, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Informational Content of the VIX Index: Dynamic Entropy Approach.

Joanna Olbryś1, Dawid Toczydłowski1

  • 1Faculty of Computer Science, Bialystok University of Technology, Wiejska 45a, 15-351 Białystok, Poland.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary

The informational content of the CBOE Volatility Index (VIX Index), the "investor fear gauge," significantly changes during market turmoil. This study confirms VIX Index information content varies across major global events.

Keywords:
STSAShannon entropyVIX Indexdiscretizationinformation theoryrolling-window

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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Area of Science:

  • Quantitative Finance
  • Financial Econometrics
  • Information Theory

Background:

  • The CBOE Volatility Index (VIX Index) is a key indicator of market sentiment, often called the "investor fear gauge."
  • Its behavior during turbulent periods is crucial for understanding market dynamics and investor psychology.
  • Existing literature highlights the VIX Index's unique role compared to other financial instruments.

Purpose of the Study:

  • To quantitatively assess the informational content of the VIX Index during significant historical events.
  • To test the hypothesis that the VIX Index's informational content fluctuates across different crisis periods.
  • To analyze the VIX Index's dynamic evolution using information theory metrics.

Main Methods:

  • Application of information theory, specifically normalized Shannon entropy.
  • Utilizing a rolling-window dynamic approach to analyze time-series data.
  • Examining the VIX Index's informational content during the Global Financial Crisis, COVID-19 pandemic, and the Trump inauguration period.

Main Results:

  • The study found that the informational content of the VIX Index does vary substantially across the analyzed turbulent periods.
  • Empirical findings indicate that entropy values are sensitive to the chosen discretization methods.
  • The results support the research hypothesis regarding the fluctuating informational content of the VIX Index.

Conclusions:

  • The VIX Index's informational content is not static and demonstrably changes during periods of market stress and significant global events.
  • The methodology employed provides robust insights into the VIX Index's dynamic nature.
  • The observed sensitivity to discretization aligns with and complements existing academic findings in financial econometrics.