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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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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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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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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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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Some new surprises in chaos.

Leonid A Bunimovich1, Luz V Vela-Arevalo2

  • 1ABC Program, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

Chaos (Woodbury, N.Y.)
|October 3, 2015
PubMed
Summary

This study reviews chaotic dynamics, proving a new theorem dual to Poincaré

Area of Science:

  • Dynamical Systems Theory
  • Chaos Theory

Background:

  • Chaos theory explores complex systems where order is sought.
  • Understanding chaotic dynamics is crucial for various scientific fields.

Purpose of the Study:

  • To review recent findings in chaotic dynamics.
  • To present a new theorem dual to the Poincaré recurrence theorem.
  • To investigate chaotic focusing billiards that violate established chaos conditions.

Main Methods:

  • Review of recent literature on chaotic dynamics.
  • Mathematical proof of a new recurrence theorem.
  • Numerical simulations of chaotic systems.
  • Analysis of chaotic focusing billiards.

Main Results:

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  • Demonstration that certain phase space regions in chaotic systems are visited earlier.
  • Identification of a new class of chaotic focusing billiards.
  • These billiards violate necessary conditions for chaos in similar systems.

Conclusions:

  • The findings contribute to a deeper understanding of chaotic system behavior.
  • The new theorem offers a novel perspective on recurrence in dynamical systems.
  • The identified billiards challenge existing theories on the necessary conditions for chaos.