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First Passage Times in Compact Domains Exhibit Biscaling.

Talia Baravi1, David A Kessler2, Eli Barkai1

  • 1Bar-Ilan University, Department of Physics, Institute of Nanotechnology and Advanced Materials, Ramat Gan 52900, Israel.

Physical Review Letters
|April 11, 2025
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Summary
This summary is machine-generated.

First passage time statistics in large systems show biscaling behavior. This study introduces a biscaling theory for confined processes, unifying short and long timescale dynamics for accurate diffusion analysis.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • First passage time (FPT) is crucial for understanding diffusion-controlled reactions and particle dynamics.
  • Large systems often display biscaling behavior in FPT, defying single-timescale analysis.
  • Existing models struggle to capture the full spectrum of FPT statistics across diverse systems.

Purpose of the Study:

  • To develop a comprehensive biscaling theory for the probability density function of first passage times.
  • To unify the description of FPT statistics across short and long timescales.
  • To provide a framework applicable to confined compact processes in various domains and geometries.

Main Methods:

  • Development of a novel biscaling theory for FPT probability density functions.
  • Inclusion of two distinct scaling functions: one for initial dynamics and one for finite-size effects.
  • Application of the theory to analyze diverse scenarios, including external forces and resetting mechanisms.

Main Results:

  • The proposed theory successfully describes FPT statistics across all timescales.
  • It captures initial dynamics in unbounded systems and finite-size effects in confined systems.
  • The framework is validated for active, thermal, and non-equilibrium steady-state scenarios.

Conclusions:

  • The biscaling theory offers a complete framework for understanding FPT statistics in confined systems.
  • It reconciles short-time and long-time dynamics, providing a unified perspective.
  • This work advances the study of diffusion processes in complex and realistic settings.