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Entropy Alternatives for Equilibrium and Out-of-Equilibrium Systems.

Eugenio E Vogel1,2, Francisco J Peña3, Gonzalo Saravia4

  • 1Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco 4811230, Chile.

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Summary
This summary is machine-generated.

We introduce non-repeatability and mutability, new measures for complex systems dynamics. Sorted mutability reveals critical system behaviors, offering insights beyond traditional entropy.

Keywords:
Monte Carlo simulationShannon entropycritical phenomenamutabilityseismic time seriesstatistical mechanics

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Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Dynamical Systems Theory

Background:

  • Traditional entropy measures often overlook temporal data ordering.
  • Dynamical entropy, like mutability, has been used in statistical physics for sequential data.
  • Analyzing complex systems requires methods sensitive to temporal dynamics.

Purpose of the Study:

  • Introduce a novel entropy-related function, non-repeatability, for complex systems.
  • Extend mutability by introducing sorted mutability for ordered data.
  • Evaluate the utility of these measures using benchmark systems and compare with Shannon entropy.

Main Methods:

  • Definition and calculation of non-repeatability and sorted mutability.
  • Application to Monte Carlo simulations of magnetic moments on a square lattice.
  • Analysis of seismic time series data from the USGS catalog.
  • Comparison with Shannon entropy to highlight differences in temporal sensitivity.

Main Results:

  • Non-repeatability and mutability demonstrate sensitivity to the temporal order of data.
  • Sorted mutability provides additional insights into the critical behavior of the studied systems.
  • The proposed measures offer a complementary perspective to traditional entropy definitions.

Conclusions:

  • Non-repeatability and sorted mutability are valuable tools for analyzing dynamical behaviors in complex systems.
  • These measures capture information related to temporal ordering, which is missed by static entropy measures.
  • The findings suggest potential applications in diverse fields studying time-dependent phenomena.