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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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Associating an Entropy with Power-Law Frequency of Events.

Evaldo M F Curado1, Fernando D Nobre1, Angel Plastino2

  • 1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil.

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Summary

Natural phenomena like earthquakes and forest fires follow power laws and are linked to Tsallis entropy (S q). Key parameters include the entropic index (q) and ground-state energy (ε₀), offering insights into complex system dynamics.

Keywords:
generalized entropiesinformation theorynonextensive thermostatisticsself-organized criticality

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Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Information Theory

Background:

  • Many natural systems exhibit power-law frequency distributions within specific validity ranges.
  • These power-law phenomena are often associated with energy spectra.
  • A connection exists between these natural events and Tsallis entropy (S q).

Purpose of the Study:

  • To explore the relationship between power-law distributed natural events and Tsallis entropy.
  • To identify and analyze key parameters governing these phenomena.
  • To provide a framework for deeper understanding using information theory.

Main Methods:

  • Analysis of power-law distributions in natural systems.
  • Association with energy spectra and Tsallis entropy (S q).
  • Identification of the entropic index (q) and ground-state energy (ε₀) as key parameters.

Main Results:

  • Power-law phenomena are intrinsically linked to Tsallis entropy (S q).
  • The entropic index (q) directly relates to the distribution's power.
  • Processes occur at a temperature T q, where k T q ∝ ε₀, analogous to self-organized criticality.
  • Estimated entropic index (q) and temperature (T q) for examples like earthquakes and forest fires.

Conclusions:

  • Tsallis entropy provides a powerful framework for understanding power-law distributed natural phenomena.
  • Key parameters like the entropic index (q) and ground-state energy (ε₀) offer new analytical perspectives.
  • This approach facilitates deeper insights through information theory and optimization.