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Related Concept Videos

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.
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...
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...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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...

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

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Using recurrences to characterize the hyperchaos-chaos transition.

Everton G Souza1, Ricardo L Viana, Sérgio R Lopes

  • 1Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, Paraná, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
PubMed
Summary

We introduce recurrence quantification analysis to detect the transition from chaos to hyperchaos using time series data. This method works even without knowing the system

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Rapid PCR Thermocycling using Microscale Thermal Convection
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Published on: March 5, 2011

Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Science
  • Time Series Analysis

Background:

  • Hyperchaos is defined by multiple positive Lyapunov exponents in dynamical systems.
  • Identifying the chaos-hyperchaos transition typically requires knowledge of system equations to track Lyapunov exponents.
  • Analyzing time series data alone presents challenges for characterizing this transition.

Purpose of the Study:

  • To develop a method for characterizing the chaos-hyperchaos transition using only time series data.
  • To apply recurrence quantification analysis (RQA) for detecting this transition.
  • To demonstrate the method's applicability to systems with unknown dynamical equations.

Main Methods:

  • Utilized recurrence quantification analysis (RQA) applied to time series data.
  • Constructed recurrence plots from the time series.
  • Analyzed changes in recurrence properties to identify the transition point.

Main Results:

  • Successfully characterized the chaos-hyperchaos transition using RQA on time series.
  • Demonstrated the method's effectiveness on coupled chaotic piecewise-linear maps and Chua-Matsumoto circuits.
  • Showcased the robustness of RQA for systems where dynamical equations are unknown.

Conclusions:

  • Recurrence quantification analysis provides a viable method for detecting chaos-hyperchaos transitions from time series.
  • This approach overcomes limitations of traditional methods that require system equations.
  • The proposed method is broadly applicable to diverse dynamical systems.