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Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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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.
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Entropy and the Second Law of Thermodynamics01:20

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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.
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Entropy01:18

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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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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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Wald-Wolfowitz Runs Test II01:17

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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
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Standard Entropy Change for a Reaction03:00

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Related Experiment Video

Updated: Dec 17, 2025

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Transfer entropy rate through Lempel-Ziv complexity.

Juan F Restrepo1,2, Diego M Mateos2,3,4, Gastón Schlotthauer1,2

  • 1Laboratorio de Señales y Dinámicas no Lineales, Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática, CONICET-UNER, Entre Ríos, Argentina.

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Summary

This study introduces a new, computationally inexpensive method to estimate transfer entropy rate, a measure of information flow between systems. The Lempel-Ziv complexity-based approach accurately assesses information exchange direction and strength, even with limited data.

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Area of Science:

  • Information theory
  • Dynamical systems analysis
  • Complexity science

Background:

  • Transfer entropy and transfer entropy rate quantify information exchange between dynamical systems.
  • Existing estimation methods can be computationally expensive or assume specific data models.
  • Assessing causality and information flow is crucial in various scientific fields.

Purpose of the Study:

  • To present a novel, computationally efficient methodology for estimating the transfer entropy rate.
  • To utilize Lempel-Ziv complexity for assessing information flow between systems.
  • To overcome limitations of existing transfer entropy estimation techniques.

Main Methods:

  • Developed a methodology to estimate transfer entropy rate using Lempel-Ziv complexity.
  • Applied the method to discrete time series data from two systems.
  • Did not assume any underlying data model for the systems.

Main Results:

  • The Lempel-Ziv complexity-based method is computationally inexpensive.
  • The methodology accurately estimates the transfer entropy rate from single discrete series.
  • Simulations on unidirectional coupled systems demonstrated effective assessment of information flow direction and strength.
  • The method provides reliable estimations even for short time series.

Conclusions:

  • The proposed Lempel-Ziv complexity-based methodology offers an efficient and model-independent approach to estimate transfer entropy rate.
  • This method is suitable for analyzing information flow in complex dynamical systems, particularly with limited data.
  • The findings suggest a valuable new tool for causality and information exchange studies.