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Related Concept Videos

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...
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...
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...
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...

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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Complexity-entropy causality plane as a complexity measure for two-dimensional patterns.

Haroldo V Ribeiro1, Luciano Zunino, Ervin K Lenzi

  • 1Departamento de Física and National Institute of Science and Technology for Complex Systems, Universidade Estadual de Maringá, Maringá, Brazil. hvr@dfi.uem.br

Plos One
|August 24, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new method to measure complexity in images and higher-dimensional data, extending permutation entropy. The technique successfully analyzes fractal landscapes, liquid crystal phases, and Ising surfaces, proving its versatility.

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Area of Science:

  • Physics
  • Information Theory
  • Data Analysis

Background:

  • Complexity measures are crucial for understanding complex systems.
  • Existing methods primarily focus on one-dimensional data, limiting analysis of higher-dimensional data like images.
  • A gap exists in easily applicable complexity measures for multi-dimensional patterns.

Purpose of the Study:

  • To bridge the gap in complexity analysis for two-dimensional and higher-dimensional data.
  • To develop a numerical procedure for evaluating the complexity of multi-dimensional patterns.
  • To validate the proposed method using diverse numerical and empirical datasets.

Main Methods:

  • Extension of permutation entropy combined with a relative entropic index.
  • Development of a numerical procedure for calculating complexity in higher dimensions.
  • Application to fractal landscapes, liquid crystal textures, and Ising surfaces.

Main Results:

  • The method successfully analyzed fractal landscapes, correlating with the Hurst exponent.
  • It accurately identified nematic-isotropic-nematic phase transitions in liquid crystal textures.
  • The approach distinguished different liquid crystal phases and identified the critical temperature in Ising surfaces, demonstrating stability.

Conclusions:

  • The proposed method effectively quantifies complexity in multi-dimensional patterns.
  • It offers a versatile tool for analyzing diverse complex systems, including phase transitions and critical phenomena.
  • The numerical procedure is easily implementable and validated across various scientific domains.