Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects

TL;DR

This paper investigates how finite-rate thermal quenches influence the Mpemba and Kovacs effects within a time-delayed Newton's law of cooling framework, revealing conditions under which these memory effects are enhanced or suppressed.

Contribution

It extends previous models by incorporating finite-rate quenches, showing their impact on the persistence and amplification of the Mpemba and Kovacs effects in thermal relaxation.

Findings

Genuine Mpemba effect is absent under finite-rate quenches with identical thermal environments.

Small quench durations allow the Mpemba effect to persist with slight enhancement.

The Kovacs effect is significantly amplified with increased waiting time and quench duration.

Abstract

The Mpemba and Kovacs effects are two notable memory phenomena observed in nonequilibrium relaxation processes. In a recent study [Phys.~Rev.~E \textbf{109}, 044149 (2024)], these effects were analyzed within the framework of the time-delayed Newton's law of cooling under the assumption of instantaneous temperature quenches. Here, the analysis is extended to incorporate finite-rate quenches, characterized by a nonzero quench duration $\sigma$. The results indicate that a genuine Mpemba effect is absent under finite-rate quenches if both samples experience the same thermal environment during the quenching process. However, if $\sigma$ remains sufficiently small, the deviations in the thermal environment stay within an acceptable range, allowing the Mpemba effect to persist with a slightly enhanced magnitude. In contrast, the Kovacs effect is significantly amplified, with the transient hump in the temperature evolution becoming more pronounced as both the waiting time and $\sigma$ increase. These findings underscore the importance of incorporating finite-time effects in nonequilibrium thermal relaxation models and offer a more realistic perspective for experimental studies.