Hysteresis-Driven Radiative Mpemba Effect in Phase-Change Nanostructures

Problem Statement
The Mpemba effect, characterized by the counterintuitive phenomenon where an initially hotter system cools faster than an initially colder one, has been documented in convective, conductive, and quantum systems. However, its radiative analogue remains unexplored. This work addresses the gap in understanding anomalous thermal relaxation within the realm of thermal radiative transport, specifically moving beyond traditional conduction and convection mechanisms. The study investigates whether non-Markovian memory effects, inherent in phase-change materials, can drive a radiative Mpemba effect.

Methodology
The authors analyze a system comprising a Vanadium Dioxide (VO₂) nanoparticle of radius $R$ positioned at a distance $d$ above a Silicon Carbide (SiC) substrate. Both materials support Surface Phonon Polaritons (SPhPs), facilitating strong near-field radiative coupling. The substrate temperature ($T_{sub}$) is held constant, while the nanoparticle temperature evolves.

The theoretical framework relies on the heat balance equation, where the rate of temperature change is determined by the exchanged radiative power ($P_{sub \leftrightarrow dip}$) and the specific heat capacity ($C_p$). A critical component of the methodology is the modeling of VO₂'s phase transition. The system exhibits hysteresis in the metallic volume fraction ($f_m$) within the transition regime ($332 \text{ K} < T < 346 \text{ K}$). To capture the non-Markovian nature of this system, the authors employ a Temperature First-Order Reversal Curve (T-FORC) model. This approach accounts for the structural memory of the material, distinguishing between heating and cooling branches and preventing unrealistic instantaneous transitions.

The study derives an analytical onset condition for the Mpemba effect by expanding the temperature evolution equation around a crossing point where two trajectories (one initially hot, one initially cold) intersect. The analysis is extended to two scenarios:

1. Active Effect: A VO₂ particle interacting with a SiC substrate.
2. Passive Effect: A SiC particle interacting with a VO₂ substrate, where the memory effect is stored externally via the substrate's reflection properties.

Key Contributions

• Analytical Derivation: The paper derives a generalized condition for the radiative Mpemba effect, demonstrating that the phenomenon arises from the interplay between the derivatives of exchanged power and specific heat capacity with respect to the internal memory variable (metallic volume fraction).
• Identification of Mechanisms: The study identifies two distinct mechanisms driving the effect:
  • Latent Heat Buffering: In the active case, the latent heat associated with the phase transition creates a massive, localized peak in specific heat capacity ($C_p$). This acts as a thermal buffer, delaying the temperature decay of the trajectory traversing the steep slope of the hysteresis loop, allowing the initially hotter trajectory to overtake it.
  • External Memory Storage: In the passive case, the memory is stored in the substrate's reflection coefficients. The radiative coupling efficiency depends on the phase of the substrate, creating a "passive" Mpemba effect without intrinsic memory in the relaxing particle.
• Phase Space Mapping: Through numerical simulations, the authors map the phase space for both ordinary and inverse Mpemba effects, defining the specific initial temperature combinations ($T_{heat}$ and $T_{cool}$) and distances required for the effect to occur.

Results

• Ordinary Mpemba Effect: For a VO₂ nanoparticle ($R=100$ nm) at $d=500$ nm above a SiC substrate ($T_{sub}=300$ K), the simulations confirm that an initially hotter particle can cool faster than a colder one. This occurs when the colder particle enters the hysteresis regime and experiences a delay due to latent heat release, while the hotter particle, having not yet reached the steep slope of the cooling branch or having passed it, cools more rapidly. The intersection time $\tau$ is highly sensitive to the initial temperatures and the near-field distance.
• Inverse Mpemba Effect: By raising the substrate temperature to $T_{sub}=378$ K to induce heating, the study observes the inverse effect (colder systems heating faster). The topology of the phase space shifts, reflecting the fundamental inversion of hysteresis pathways where latent heat absorption delays the heating of the initially hotter particle.
• Passive Mpemba Effect: When a SiC particle is placed above a VO₂ substrate, the effect is observed solely due to the external memory stored in the substrate's reflection. The initially hotter SiC particle cools faster than the colder one because the metallic phase of the VO₂ substrate reflects radiation more strongly, reducing radiative coupling and slowing heat exchange compared to the dielectric phase. This effect vanishes as the distance increases to the far-field regime ($d > 1$ $\mu$m), proving its reliance on near-field coupling.
• Role of Near-Field Coupling: The study confirms that near-field coupling governs the relaxation time. While the radiative power contrast is non-negligible, the dominant factor for the Mpemba effect is the caloric channel (latent heat modulation of $C_p$).

Significance
The paper claims to translate the Mpemba effect to thermal radiative transport, establishing a new platform for observing anomalous relaxation. The significance lies in demonstrating that:

1. Memory is Central: The effect is driven by non-Markovian memory effects, either intrinsic (hysteresis in the particle) or extrinsic (reflection in the substrate).
2. Geometric Tunability: The passive variant highlights that the anomaly can be triggered solely via external memory storage, offering geometric tunability as the system transitions between near- and far-field regimes.
3. Experimental Feasibility: The chosen setup matches readily accessible experimental configurations, such as pump-probe microscopy, facilitating laboratory verification.
4. Thermal Management: The findings open avenues for exploiting material history and structural memory in radiative heat transfer, potentially serving as a cornerstone for advanced dynamic thermal management on the nanoscale. The authors suggest that the effect's magnitude could be enhanced using symmetric VO₂-VO₂ configurations or by tuning the hysteresis loop via doping (e.g., tungsten).