Mpemba as an Emergent Effect of System Relaxation

TL;DR

This paper presents a generic quantum model explaining the Mpemba effect as an emergent phenomenon of system relaxation, emphasizing the role of initial state overlap and collective behavior in producing faster relaxation.

Contribution

It introduces a universal quantum relaxation model that explains Mpemba effect as a collective emergent property, applicable to both driven and undriven systems.

Findings

Mpemba effect arises from initial state overlap with fast relaxation modes.

Anisotropic relaxation naturally leads to Mpemba effect without shared environment.

System collective behavior is key to the emergence of MpE.

Abstract

The Mpemba effect (MpE), where a far-from-equilibrium state of a system relaxes faster compared to a state closer to it, is a well-known counterintuitive phenomenon in classical and quantum systems. Various system-specific theories have been proposed to explain this anomalous behavior in driven systems, though the fundamental mechanism of MpE in undriven systems, where MpE was first observed, remains unresolved. This paper provides a generic model of MpE for a quantum system following Markovian relaxation dynamics, regardless of system structure or environment. The key lies in the overlap of initial states with the fast relaxation mode; here, the constituents create a fast decay mode via interaction through the shared environment to show MpE, indicating MpE happens due to the collective behavior of the system. I also show that a system with anisotropic relaxation naturally exhibits MpE, even without a shared environment among the particles.