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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • First passage under restart is a framework for diverse phenomena.
  • Identifying unifying principles has been challenging due to varied mechanisms.
  • Previous work showed universality in optimal, constant rate restart processes.

Purpose of the Study:

  • To develop a generic approach for first passage under restart.
  • To identify unifying principles across different restart mechanisms and processes.
  • To demonstrate the universality of key features in diffusion under restart.

Main Methods:

  • Developed a generalized mathematical framework for first passage under restart.
  • Analyzed the interplay between restart mechanisms and underlying processes.
  • Focused on diffusion as a representative model system.

Main Results:

  • The generic approach successfully unifies diverse restart phenomena.
  • Key features of diffusion under restart were shown to be completely universal.
  • The framework accommodates arbitrarily complex processes and restart mechanisms.

Conclusions:

  • A unified understanding of first passage under restart is now achievable.
  • Universality is a key characteristic of diffusion under restart.
  • The developed approach provides a powerful tool for analyzing complex systems with restart.