Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915281870258176 |
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| author | Santos, Andrés |
| author_facet | Santos, Andrés |
| contents | 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 $σ$. 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 $σ$ 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 $σ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects Santos, Andrés Statistical Mechanics Materials Science Soft Condensed Matter Classical Physics Fluid Dynamics 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 $σ$. 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 $σ$ 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 $σ$ 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. |
| title | Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects |
| topic | Statistical Mechanics Materials Science Soft Condensed Matter Classical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2502.13665 |