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Related Concept Videos

Entropy02:39

Entropy

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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...
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Entropy01:18

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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.
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Consider an infinitesimal step in the expansion, which...
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Entropy Changes Accompanying Specific Processes01:21

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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...
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The Entropy as a State Function01:14

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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...
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Entropy Change in Reversible Processes01:10

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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.
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Standard Entropy Change for a Reaction03:00

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Perceived Complexity as Normalized, Integrated, Localized Shannon Entropy.

Sébastien Berquet1,2, Norberto M Grzywacz3

  • 1Department of Biology, Loyola University Chicago, Chicago, IL 60660, USA.

Entropy (Basel, Switzerland)
|March 28, 2026
PubMed
Summary
This summary is machine-generated.

Perceived complexity in sensory processing is better measured by integrating localized Shannon entropy (LSE) at low spatial scales, not by estimating distributions from the entire signal at once.

Keywords:
Shannon entropyaestheticsartistic paintingscolorimage statisticsluminancenatural imagesperceived complexityspatial scalesurban images

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Area of Science:

  • Cognitive Neuroscience
  • Computational Neuroscience
  • Visual Art Analysis

Background:

  • Perceived complexity is crucial for sensory brain function, indicating information processing resource demands.
  • A recent measure defined perceived complexity as normalized Shannon entropy, but this method faced limitations.
  • Estimating probability distributions from the entire sensory signal at once proved incompatible with perceived complexity.

Purpose of the Study:

  • To investigate the limitations of existing Shannon entropy measures for perceived complexity.
  • To propose and validate an alternative theory integrating localized Shannon entropy (LSE) for complexity measurement.
  • To explore the relationship between LSE, spatial scale, and aesthetic choices in art.

Main Methods:

  • Utilized synthetic images and abstract expressionism art to test existing complexity measures.
  • Developed a new theory based on the integration of localized Shannon entropy (LSE).
  • Measured the proposed complexity index and integrated LSE across 704 diverse images at varying spatial scales.

Main Results:

  • The estimation of probability distributions from the entire signal was incompatible with perceived complexity, even across different scales.
  • Normalized, integrated LSE at low spatial scales aligns with perceived complexity.
  • This approach revealed aesthetic choices in artworks by different artists.

Conclusions:

  • The integration of localized Shannon entropy (LSE) at low spatial scales provides a more accurate measure of perceived complexity.
  • The findings challenge previous models and offer a new perspective on sensory information processing.
  • The study demonstrates the utility of LSE in analyzing visual complexity and artistic aesthetics.