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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...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
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...

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Related Experiment Video

Updated: Jun 18, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
11:15

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

Published on: June 27, 2013

Approximate entropy for all signals.

Ki Chon1, Christopher G Scully, Sheng Lu

  • 1Department of Biomedical Engineering, SUNY Stony Brook, Stony Brook, New York City, New York, USA. ki.chon@sunysb.edu

IEEE Engineering in Medicine and Biology Magazine : the Quarterly Magazine of the Engineering in Medicine & Biology Society
|November 17, 2009
PubMed
Summary
This summary is machine-generated.

Calculating approximate entropy (ApEn) can be computationally intensive. This study introduces a new heuristic stochastic model for automatic selection of the maximum ApEn value, improving signal complexity assessment.

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Area of Science:

  • Complexity Science
  • Signal Processing
  • Biomedical Engineering

Background:

  • Approximate Entropy (ApEn) quantifies signal complexity but requires parameter selection (m, r).
  • Standard r values (0.1-0.2 std dev) may misrepresent signal complexity.
  • Maximizing ApEn across all r values improves accuracy but is computationally demanding.

Purpose of the Study:

  • To develop a computationally efficient method for selecting the optimal r value for ApEn calculation.
  • To ensure accurate assessment of signal complexity by identifying the true maximum ApEn.
  • To overcome the limitations of standard parameter choices in ApEn analysis.

Main Methods:

  • A novel heuristic stochastic model was developed for automatic ApEn maximization.
  • Monte Carlo simulations were used to derive general equations for estimating maximum ApEn.
  • The method was validated using synthetic and experimental physiological data.

Main Results:

  • The proposed method accurately estimates the maximum ApEn value for a given m.
  • It overcomes the computational burden associated with evaluating all possible r values.
  • The approach provides a more reliable interpretation of signal complexity compared to standard methods.

Conclusions:

  • The heuristic stochastic model offers an efficient and accurate way to determine maximum ApEn.
  • This method enhances the reliability of signal complexity analysis in various applications.
  • The approach addresses a key limitation in the practical application of approximate entropy.