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First-passage time for superstatistical Fokker-Planck models.

Adrián A Budini1, Manuel O Cáceres2

  • 1Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche, Avenida E. Bustillo Km 9.5, 8400 Bariloche, Argentina and Universidad Tecnológica Nacional (UTN-FRBA), Fanny Newbery 111, 8400 Bariloche, Argentina.

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This study links first-passage-time (FPT) moments to superstatistical model parameters. This provides a new method for validating superstatistical models, demonstrated with a forced Brownian particle example.

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Area of Science:

  • Statistical Physics
  • Complex Systems Dynamics

Background:

  • Superstatistical models are used to describe complex systems where parameters fluctuate.
  • The first-passage-time (FPT) problem is crucial for understanding system dynamics and escape phenomena.

Purpose of the Study:

  • To establish a connection between FPT moments and parameters in superstatistical models.
  • To develop a new method for validating superstatistical models.
  • To analyze FPT in systems with external forces.

Main Methods:

  • Utilizing Fokker-Planck equations to describe mesoscopic system dynamics.
  • Analyzing the moments of the random intensive parameter in superstatistical models.
  • Investigating the dependence of FPT moments on external forces.

Main Results:

  • A one-to-one correspondence is found between moments of the random intensive parameter and FPT moments.
  • Statistical information can be extracted from FPT moments' dependence on external forces.
  • The mean FPT for a forced Brownian particle is characterized.

Conclusions:

  • The established correspondence offers an alternative technique for validating superstatistical models.
  • The study provides insights into the dynamics of systems described by superstatistics and Fokker-Planck equations.
  • The findings are applicable to systems with and without external forces.