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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 Second Law of Thermodynamics01:14

The Second Law of Thermodynamics

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 put...
Cognitive Learning01:21

Cognitive Learning

Cognitive learning is based on purposive behavior, incidental learning, and insight learning.
E. C. Tolman's theory of purposive behavior emphasizes that much behavior is goal-directed. He argued that to understand behavior, we must look at the entire sequence of actions leading to a goal. For instance, high school students study hard, not just due to past reinforcement but also to achieve the goal of getting into a good college.
Tolman introduced the idea that behavior is influenced by...
Freud's Psychoanalytic Theory01:29

Freud's Psychoanalytic Theory

Sigmund Freud's psychoanalytic theory revolutionized psychology by introducing the idea that unconscious forces significantly shape human behavior. According to Freud, every psychological event is driven by deep-seated internal forces, often formed during early childhood. His theory, built on the premises of psychic determinism, symbolic meaning, and unconscious motivation, offers a unique perspective on the complexities of human behavior.
Freud's concept of psychic determinism asserts that...
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...

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Updated: Jun 22, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Chaos theory before Lorenz.

J Barkley Rosser1

  • 1Department of Economics, James Madison University, Harrisonburg, VA 22807, USA. rosserjb@jmu.edu

Nonlinear Dynamics, Psychology, and Life Sciences
|June 17, 2009
PubMed
Summary
This summary is machine-generated.

This study explores early scientific ideas hinting at sensitive dependence on initial conditions, a key concept in chaos theory. It traces precursors in celestial mechanics, oscillators, and economics before Edward Lorenz

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Last Updated: Jun 22, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

  • * **Chaos Theory:** Explores the study of complex systems and their sensitive dependence on initial conditions.
  • * **Fluid Dynamics:** Investigates the behavior of liquids and gases, crucial for understanding climate models.
  • * **Mathematical Modeling:** Utilizes mathematical frameworks to simulate and analyze complex phenomena.

Background:

  • * Edward Lorenz's 1963 model of climatic fluid dynamics introduced the concept of sensitive dependence on initial conditions.
  • * Precursors to this discovery can be found in various scientific disciplines, suggesting a long-standing, albeit unrecognized, presence of chaotic behavior.
  • * Ancient Greek philosophy, 19th-century mathematics, and physics laid groundwork for understanding complex dynamics.

Purpose of the Study:

  • * To investigate the historical scientific contributions that foreshadowed Edward Lorenz's discovery of sensitive dependence on initial conditions.
  • * To identify and analyze works exhibiting characteristics of chaotic systems, such as irregular dynamics and fractal attractors.
  • * To demonstrate the interdisciplinary nature of chaos theory's origins.

Main Methods:

  • * Historical literature review across disciplines including celestial mechanics, oscillator studies, and economics.
  • * Analysis of theoretical works for evidence of sensitivity to initial conditions or fractal patterns.
  • * Tracing conceptual links from ancient philosophy to modern scientific models.

Main Results:

  • * Identified precursors to sensitive dependence on initial conditions in celestial mechanics, particularly in the study of planetary orbits.
  • * Found evidence of irregular dynamic patterns and fractal-like structures in the analysis of oscillators.
  • * Observed concepts related to sensitive dependence and complex dynamics within economic theories.

Conclusions:

  • * The discovery of sensitive dependence on initial conditions by Edward Lorenz was built upon a rich history of prior scientific inquiry.
  • * Concepts related to chaos theory were present in diverse fields long before their formal recognition.
  • * Celestial mechanics, oscillator theory, and economics provided crucial conceptual groundwork for the development of chaos theory.