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Related Concept Videos

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...
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...
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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...
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...
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.
Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

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Testing pattern synchronization in coupled systems through different entropy-based measures.

Peng Li1, Chengyu Liu, Xinpei Wang

  • 1School of Control Science and Engineering, Shandong University, 17923 Jingshi Road, Jinan 250061, People's Republic of China.

Medical & Biological Engineering & Computing
|January 23, 2013
PubMed
Summary
This summary is machine-generated.

This study compares entropy measures for physiological system interactions. Multivariate multiscale entropy (MMSE) is recommended over cross sample entropy (X-SampEn) and cross fuzzy entropy (X-FuzzyEn) for analyzing complex cardiorespiratory coupling.

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Area of Science:

  • Physiological systems analysis
  • Complex systems science
  • Biomedical signal processing

Background:

  • Pattern synchronization (PS) quantifies interactions in bivariate physiological systems.
  • Entropy-based measures like cross sample entropy (X-SampEn), cross fuzzy entropy (X-FuzzyEn), and multivariate multiscale entropy (MMSE) assess PS.
  • A comprehensive comparison of these measures' consistency and distinguishability is lacking, particularly concerning parameter dependency.

Purpose of the Study:

  • To comprehensively compare the consistency and distinguishability of entropy-based measures for pattern synchronization.
  • To evaluate the suitability of X-SampEn, X-FuzzyEn, and MMSE for analyzing dynamic interactions in physiological systems.
  • To determine the reliability of these measures under varying parameter conditions, especially the threshold value 'r'.

Main Methods:

  • Simulated coupled models were used to evaluate pattern synchronization measures.
  • Consistency and distinguishability were quantified using degree of crossing (DoC) and degree of monotonicity (DoM).
  • Performance of X-SampEn, X-FuzzyEn, and MMSE was assessed across different coupled systems, including cardiorespiratory coupling.

Main Results:

  • X-SampEn and X-FuzzyEn demonstrated limited effectiveness, requiring meticulous parameter selection (threshold 'r') and are not recommended for complex physiological systems.
  • MMSE showed superior performance, exhibiting higher consistency and distinguishability (DoC and DoM) across both simulated and real physiological systems.
  • Results were validated through an analysis of cardiorespiratory coupling, confirming MMSE's robustness.

Conclusions:

  • MMSE is a more reliable and versatile measure for assessing pattern synchronization in complex physiological systems compared to X-SampEn and X-FuzzyEn.
  • The findings highlight the limitations of parameter-dependent entropy measures in intricate biological contexts.
  • MMSE provides a robust approach for understanding cardiorespiratory coupling and potentially other bivariate physiological interactions.