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Entropic form emergent from superstatistics.

Maike A F Dos Santos1,2, Fernando D Nobre2,3, Evaldo M F Curado2,3

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Summary
This summary is machine-generated.

This study introduces a modified chi-squared distribution for Beck-Cohen superstatistics, applicable to complex systems. The new model unifies q-exponential and stretched exponential distributions, expanding their use in nonequilibrium systems.

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Area of Science:

  • Statistical Physics
  • Complex Systems Theory

Background:

  • Beck-Cohen superstatistics model complex systems with varying temperatures.
  • Commonly used distributions include chi-squared and log-normal.
  • Nonequilibrium systems present challenges in statistical description.

Purpose of the Study:

  • Investigate a modified chi-squared distribution for superstatistics.
  • Introduce a generalized framework encompassing q-exponential and stretched exponential distributions.
  • Explore applications in complex systems with fluctuating parameters.

Main Methods:

  • Introduced a modified chi-squared distribution with index η (0<η≤1).
  • Analyzed the resulting superstatistics probability distribution f(β).
  • Derived an associated generalized entropic form.

Main Results:

  • The modified chi-squared distribution unifies q-exponential and stretched exponential distributions as special cases.
  • The framework is applicable to systems with temperature fluctuations.
  • A generalized entropic form was successfully derived.

Conclusions:

  • The proposed superstatistics framework offers a unified approach for describing complex systems.
  • The findings are expected to be applicable to a broad range of nonequilibrium phenomena.
  • This generalization enhances the toolkit for analyzing systems with fluctuating parameters.