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Related Concept Videos

Entropy02:39

Entropy

33.7K
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

Entropy

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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.
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...
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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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...
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The Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
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.
3.0K
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

26.0K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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On α-chaotic points and chaotic (antichaotic) families of functions.

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On Points Focusing Entropy.

Ewa Korczak-Kubiak1, Anna Loranty1, Ryszard J Pawlak1

  • 1Faculty of Mathematics and Computer Science, ódź University, Banacha 22, 90-238 ódź, Poland.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

We introduce focal entropy points to analyze the complexity of nonautonomous dynamical systems locally. Periodic systems exhibit these points, and slight system modifications can create them, impacting system distortions and approximations.

Keywords:
(asymptotical) focal entropy pointdisturbationm-dimensional manifoldnonautonomous (autonomous) dynamical systemtopological entropy

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Area of Science:

  • Dynamical Systems Theory
  • Information Theory
  • Thermodynamics

Background:

  • Entropy quantifies system complexity and is crucial in thermodynamics and information flow.
  • Existing entropy measures often consider global system behavior.
  • Understanding local entropy is vital for analyzing complex systems.

Purpose of the Study:

  • To introduce and define the concept of a focal entropy point for nonautonomous dynamical systems.
  • To investigate the local complexity of dynamical systems.
  • To analyze system distortions and approximations using the focal entropy point concept.

Main Methods:

  • Definition of (asymptotical) focal entropy points.
  • Analysis of system complexity around specific points.
  • Examination of system distortions and approximations in relation to focal entropy points.

Main Results:

  • The introduction of (asymptotical) focal entropy points provides a localized measure of system complexity.
  • Periodic systems operating in a closed unit interval are shown to possess an asymptotical focal entropy point.
  • Even minor alterations to a system can induce the formation of focal entropy points.

Conclusions:

  • Focal entropy points offer a novel perspective on the local complexity of nonautonomous dynamical systems.
  • The existence of focal entropy points in periodic systems highlights their significance.
  • The sensitivity of focal entropy point emergence to system modifications has implications for system analysis and modeling.