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This study explores the Mpemba effect in active systems, finding that activity can suppress or induce this phenomenon. Researchers observed an oscillatory Mpemba effect due to complex system dynamics.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • The Mpemba effect, where warmer water freezes faster than colder water, is observed in equilibrium systems.
  • Nonequilibrium systems with broken detailed balance exhibit unique dynamic behaviors.
  • Active matter systems, characterized by self-propulsion, are inherently out of equilibrium.

Purpose of the Study:

  • To investigate the Mpemba effect in a nonequilibrium Markov chain model of active random walkers.
  • To understand how broken detailed balance, introduced by activity, influences the Mpemba effect.
  • To explore novel phenomena like oscillatory Mpemba effect in active systems.

Main Methods:

  • Development of a nonequilibrium Markov chain model simulating active random walkers in a discrete energy landscape.
  • Analysis of system relaxation dynamics under conditions of broken detailed balance.
  • Investigation of the role of complex eigenvalues in the relaxation spectrum.

Main Results:

  • The activity in the system can either suppress or induce the Mpemba effect.
  • An oscillatory Mpemba effect was observed, characterized by multiple crossings of relaxation trajectories.
  • Complex eigenvalues emerging due to activity were identified as the cause of the oscillatory behavior.

Conclusions:

  • Broken detailed balance in active systems can lead to anomalous relaxation dynamics and modified Mpemba effect phenomena.
  • The study demonstrates that activity can induce an oscillatory Mpemba effect, a novel observation.
  • This research provides a framework for studying the Mpemba effect in biologically relevant active systems.