Anomalous cooling and Mpemba effect in an oscillatory inductor-resistor-capacitor thermoelectric network and its inverse

Abstract

Anomalous cooling or heating implies attractive underlying thermal physics, and the Mpemba effect and its inverse are typical examples. Most existing explanations for such phenomena are based on microscopic Markovian models that quantify relaxation using distance measures such as total variation distance or Kullback-Leibler divergence. Here, we propose a macroscopic network system to observe and analyze the Mpemba effect and its inverse by connecting a thermoelectric module with a body and a reservoir at different initial temperatures. Normal cooling and anomalous cooling can be switched in such a setup, and oscillatory behaviors of temperature, current, and heat flow are found to be the key for achieving the Mpemba effect and its inverse. With an unambiguous definition of the criteria, the occurrence domain of the Mpemba effect is sketched in terms of initial temperature, thermoelectric Figure-of-Merit, and the inductance. This work provides a macroscopic network system to understand the Mpemba effect, and offers a more flexible and dynamic way for thermal management and energy conversion.

Keywords

Mpemba effect / anomalous cooling / inductor-resistor-capacitor networks

References

[1] Chen G. Non-Fourier phonon heat conduction at the microscale and nanoscale. Nat Rev Phys. 2021; 3(8):555-569.

[2] Li X, Lee S. Crossover of ballistic, hydrodynamic, and diffusive phonon transport in suspended graphene. Phys Rev B. 2019; 99(8):085202.

[3] Hu R, Chen Z, Kim SK. Research. Can thermal nonreciprocity help radiative cooling? 2024; 7:563.

[4] Chen Z, Yu S, Ma J, Xie B, Kim SK, Hu R. Wavelength-selective thermal nonreciprocity barely improves sky radiative cooling. Fundam Res. 2026; 6(2):718-724.

[5] Cho JW, Lee YJ, Kim JH, Hu R, Lee E, Kim SK. Directional radiative cooling via exceptional epsilon-based microcavities. ACS Nano. 2023; 17(11):10442-10451.

[6] Mpemba EB, Osborne DG. Cool? Phys Educ. 1969; 4(3):172-175.

[7] Jeng M. The Mpemba effect: When can hot water freeze faster than cold? Am J Phys. 2006; 74(6):514-522.

[8] Lu Z, Raz O. Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse. Proc Natl Acad Sci U S A. 2017; 114(20):5083-5088.

[9] Klich I, Raz O, Hirschberg O, Vucelja M. Mpemba index and anomalous relaxation. Phys Rev X. 2019; 9(2):021060.

[10] Schwarzendahl FJ, Löwen H. Anomalous cooling and overcooling of active colloids. Phys Rev Lett. 2022; 129(13):138002.

[11] Kumar A, Bechhoefer J. Exponentially faster cooling in a colloidal system. Nature. 2020; 584(7819):64-68.

[12] Kumar A, Chétrite R, Bechhoefer J. Anomalous heating in a colloidal system. Proc Natl Acad Sci U S A. 2022; 119(5):e2118484119.

[13] Hu C, Li J, Huang S, Li H, Luo C, Chen J, et al. Conformation directed mpemba effect on polylactide crystallization. Cryst Growth Des. 2018; 18(10):5757-5762.

[14] Lasanta A, Vega Reyes F, Prados A, Santos A. When the hotter cools more quickly: Mpemba effect in granular fluids. Phys Rev Lett. 2017; 119(14):148001.

[15] Baity-Jesi M, Calore E, Cruz A, Fernandez LA, Gil-Narvión JM, Gordillo-Guerrero A, et al. The Mpemba effect in spin glasses is a persistent memory effect. Proc Natl Acad Sci U S A. 2019; 116(31):15350-15355.

[16] Carollo F, Lasanta A, Lesanovsky I. Exponentially accelerated approach to stationarity in Markovian open quantum systems through the mpemba effect. Phys Rev Lett. 2021; 127(6):060401.

[17] Chatterjee AK, Takada S, Hayakawa H. Quantum mpemba effect in a quantum dot with reservoirs. Phys Rev Lett. 2023; 131(8):080402.

[18] Moroder M, Culhane O, Zawadzki K, Goold J. Thermodynamics of the quantum mpemba effect. Phys Rev Lett. 2024; 133(14):140404.

[19] Nava A, Egger R. Mpemba effects in open nonequilibrium quantum systems. Phys Rev Lett. 2024; 133(13):136302.

[20] Liu S, Zhang HK, Yin S, Zhang SX. Symmetry restoration and quantum mpemba effect in symmetric random circuits. Phys Rev Lett. 2024; 133(14):140405.

[21] Joshi LK, Franke J, Rath A, Ares F, Murciano S, Kranzl F, et al. Observing the quantum mpemba effect in quantum simulations. Phys Rev Lett. 2024; 133:010402.

[22] Gal A, Raz O. Precooling strategy allows exponentially faster heating. Phys Rev Lett. 2020; 124(6):060602.

[23] Burridge HC, Linden PF. Questioning the Mpemba effect: Hot water does not cool more quickly than cold. Sci Rep. 2016; 6:37665.

[24] Teza G, Yaacoby R, Raz O. Relaxation shortcuts through boundary coupling. Phys Rev Lett. 2023; 131:017101.

[25] Pemartín IG, Mompó E, Lasanta A, Martín-Mayor V, Salas J. Shortcuts of freely relaxing systems using equilibrium physical observables. Phys Rev Lett. 2024; 132(11):117102.

[26] Rylands C, Klobas K, Ares F, Calabrese P, Murciano S, Bertini B. Microscopic origin of the quantum mpemba effect in integrable systems. Phys Rev Lett. 2024; 133:010401.

[27] Mirabedin SM, Farhadi F. Numerical investigation of solidification of single droplets with and without evaporation mechanism. Int J Refrig. 2017; 73:219-225.

[28] Vynnycky M, Kimura S. Can natural convection alone explain the Mpemba effect? Int J Heat Mass Transf. 2015; 80:243-255.

[29] Auerbach D. Supercooling and the Mpemba effect: When hot water freezes quicker than cold. Am J Phys. 1995; 63(10):882-885.

[30] Zhang X, Huang Y, Ma Z, Zhou Y, Zhou J, Zheng W, et al. Hydrogen-bond memory and water-skin supersolidity resolving the Mpemba paradox. Phys Chem Chem Phys. 2014; 16(42):22995-23002.

[31] Aharony Shapira S, Shapira Y, Markov J, Teza G, Akerman N, Raz O, et al. Inverse mpemba effect demonstrated on a single trapped ion qubit. Phys Rev Lett. 2024; 133:010403.

[32] Ibáñez M, Dieball C, Lasanta A, Godec A, Rica RA. Heating and cooling are fundamentally asymmetric and evolve along distinct pathways. Nat Phys. 2024; 20(1):135-141.

[33] Van Vu T, Hayakawa H. Thermomajorization mpemba effect. Phys Rev Lett. 2025; 134(10):107101.

[34] Domenicali CA. Irreversible thermodynamics of thermoelectric effects in inhomogeneous, anisotropic media. Phys Rev. 1953; 92(4):877-881.

[35] Schilling A, Zhang X, Bossen O. Heat flowing from cold to hot without external intervention by using a “thermal inductor”. Sci Adv. 2019; 5(4):eaat9953.

[36] Goupil C, Seifert W, Zabrocki K, Müller E, Snyder GJ. Thermodynamics of thermoelectric phenomena and applications. Entropy. 2011; 13(8):1481-1517.

[37] Xue TW, Guo ZY. Thermoelectric cycle and the second law of thermodynamics. Entropy. 2023; 25(1):155.