Mpemba Effect in Parametrically Driven Coupled Oscillators under White and Colored Noise
Abstract
We study the Mpemba effect in a pair of linearly coupled harmonic oscillators, one of which is parametrically driven and coupled to an independent thermal bath. Using the covariance-matrix formalism, we derive the relaxation dynamics under both Gaussian white noise and Lorentzian colored noise, including single-channel and dual-channel noise embedding. We characterize relaxation through the Frobenius distance to the steady state and through the projection onto the slowest mode of the dynamical generator. Our results show that parametric driving provides the primary control knob for anomalous relaxation: as the drive approaches the stability boundary, the Mpemba crossing time decreases systematically. Colored noise further enhances the effect, with dual-oscillator Lorentzian noise producing a stronger reduction in the crossing time than single-oscillator noise and enlarging the parameter region where the Mpemba effect occurs. Nevertheless, the slow-mode structure of the drift matrix remains the dominant mechanism, while the influence of colored noise is secondary and mainly quantitative. We show that the Mpemba crossing time decreases as the system approaches the parametric stability boundary and that Lorentzian colored noise enlarges the region in the parametric and coupling strength plane where the Mpemba effect is observed.
Related
- Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillator
- Effect of Colored Noise on Coupled Thermoacoustic Oscillators
- Second harmonic phase locking and synchronization blockade in quadratically coupled driven quantum van der Pol oscillators
- Stability of Solitons in the Parametrically Driven and Damped Nonlinear Schrödinger Equation in Arbitrary Dimension
- Oscillatory instability of subcritical stationary solutions in the parametrically driven, damped nonlinear Dirac equation
BibTeX
@misc{pahlevani2026mpemba,
title = {{Mpemba Effect in Parametrically Driven Coupled Oscillators under White and Colored Noise}},
author = {Aref Pahlevani and Morteza Rafiee and Mehdi Ansari-rad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.01723},
eprint = {2605.01723},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.01723},
note = {CC0},
}
RIS
TY - UNPB
TI - Mpemba Effect in Parametrically Driven Coupled Oscillators under White and Colored Noise
AU - Aref Pahlevani
AU - Morteza Rafiee
AU - Mehdi Ansari-rad
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.01723
UR - https://arxiv.org/abs/2605.01723
AB - We study the Mpemba effect in a pair of linearly coupled harmonic oscillators, one of which is parametrically driven and coupled to an independent thermal bath. Using the covariance-matrix formalism, we derive the relaxation dynamics under both Gaussian white noise and Lorentzian colored noise, including single-channel and dual-channel noise embedding. We characterize relaxation through the Frobenius distance to the steady state and through the projection onto the slowest mode of the dynamical generator. Our results show that parametric driving provides the primary control knob for anomalous relaxation: as the drive approaches the stability boundary, the Mpemba crossing time decreases systematically. Colored noise further enhances the effect, with dual-oscillator Lorentzian noise producing a stronger reduction in the crossing time than single-oscillator noise and enlarging the parameter region where the Mpemba effect occurs. Nevertheless, the slow-mode structure of the drift matrix remains the dominant mechanism, while the influence of colored noise is secondary and mainly quantitative. We show that the Mpemba crossing time decreases as the system approaches the parametric stability boundary and that Lorentzian colored noise enlarges the region in the parametric and coupling strength plane where the Mpemba effect is observed.
ER -