Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillator
Abstract
For two Gaussian preparations of a detuned degenerate parametric amplifier below threshold, the trace distance shows a lasting Mpemba reversal, whereas the relative entropy eventually restores the initial order and the Hilbert--Schmidt distance alternates indefinitely. All three diagnostics agree on the initial order, and these orders persist on open sets of preparations and quadratic generators. The disagreement is possible because a real relaxation mode and a complex-conjugate pair share the leading decay rate, a coincidence that holds for any single-mode quadratic oscillator with linear damping in the elliptic regime. Number symmetry hides their competition in the undriven trace-distance tail, and parametric driving exposes it. Near a pure stationary state, the relative entropy strongly weights changes of the symplectic eigenvalue, which approximately follow the nonoscillating energy deviation; thermal occupation weakens this preference. A first-order splitting rule shows that weak number dephasing and two-photon loss favor the real branch, whereas a Kerr interaction with the same sign as the detuning favors the pair. We quantify the thermal-occupation and dephasing tolerances and estimate the measurement precision needed to observe the disagreement. Whether a Mpemba reversal is lasting therefore depends on the diagnostic and on the observation window.
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BibTeX
@misc{he2026diagnosticdependent,
title = {{Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillator}},
author = {Shu He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36663},
eprint = {2610.36663},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36663},
}
RIS
TY - UNPB
TI - Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillator
AU - Shu He
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36663
UR - https://arxiv.org/abs/2610.36663
AB - For two Gaussian preparations of a detuned degenerate parametric amplifier below threshold, the trace distance shows a lasting Mpemba reversal, whereas the relative entropy eventually restores the initial order and the Hilbert--Schmidt distance alternates indefinitely. All three diagnostics agree on the initial order, and these orders persist on open sets of preparations and quadratic generators. The disagreement is possible because a real relaxation mode and a complex-conjugate pair share the leading decay rate, a coincidence that holds for any single-mode quadratic oscillator with linear damping in the elliptic regime. Number symmetry hides their competition in the undriven trace-distance tail, and parametric driving exposes it. Near a pure stationary state, the relative entropy strongly weights changes of the symplectic eigenvalue, which approximately follow the nonoscillating energy deviation; thermal occupation weakens this preference. A first-order splitting rule shows that weak number dephasing and two-photon loss favor the real branch, whereas a Kerr interaction with the same sign as the detuning favors the pair. We quantify the thermal-occupation and dephasing tolerances and estimate the measurement precision needed to observe the disagreement. Whether a Mpemba reversal is lasting therefore depends on the diagnostic and on the observation window.
ER -