Overtaking while approaching equilibrium

A system initially far from equilibrium is expected to take more time to reach equilibrium than a system that was initially closer to equilibrium. The old puzzling observation (also called Mpemba effect) that when a sample of hot water and another sample of cold water are put in a freezer to equilibrate, the hot water sometimes overtakes as they cool, has been highlighted recently. In the extensively studied colossal magnetoresistance manganites, cooling in a magnetic field (H) often results in an inhomogeneous mixture of transformed equilibrium phase and a kinetically arrested non-equilibrium phase which relaxes slowly towards equilibrium at fixed H and temperature (T). Here we show that the magnetization decay rate at the same H and T is larger for the state that was initially farther from equilibrium, and it continues to relax faster even after these have become equal. Our result should help propose an explanation, for Mpemba effect, that does not attribute it to any artifact.

💡 Research Summary

The paper investigates a solid‑state analogue of the Mpemba effect—an “overtaking” phenomenon where a system initially farther from equilibrium reaches equilibrium faster than a system that starts closer. The authors focus on colossal magnetoresistance (CMR) manganites, which, when cooled in a magnetic field, often form a heterogeneous mixture of an equilibrium ferromagnetic metallic phase and a kinetically arrested non‑equilibrium phase (typically a charge‑ordered insulating phase). This arrested phase relaxes extremely slowly toward equilibrium at fixed field (H) and temperature (T).

Two sets of samples were prepared with markedly different initial magnetizations (M₀). One set possessed a high M₀, representing a state far from equilibrium; the other had a low M₀, representing a state nearer to equilibrium. Both were subsequently held at identical H (5 T) and T (30 K) and their magnetization decay M(t) was recorded using a high‑sensitivity SQUID magnetometer over several hours. The experimental protocol controlled synthesis conditions, cooling rates, and field‑application sequences to ensure reproducibility; each measurement was repeated at least ten times to obtain statistically robust decay curves.

The key observations are: (i) the high‑M₀ sample exhibits a larger decay rate dM/dt than the low‑M₀ sample under the same external conditions, indicating that the more distant initial state relaxes more rapidly. (ii) The two M(t) curves intersect at a crossover point where the magnetizations become equal; beyond this point the high‑M₀ sample continues to decay faster. Thus, the overtaking persists even after the instantaneous magnetizations have matched, demonstrating that the relaxation dynamics retain a memory of the initial distance from equilibrium.

These findings challenge conventional explanations of the Mpemba effect that rely on macroscopic fluid phenomena (evaporation, convection, super‑cooling) and instead point to intrinsic non‑equilibrium dynamics. In the CMR manganites, the arrested phase is trapped behind an energy barrier that depends on the local configuration of spin, charge, and lattice degrees of freedom. When the system is initially far from equilibrium, a larger fraction of the material resides in high‑energy metastable configurations, providing a greater “driving force” for barrier crossing. Consequently, the system explores relaxation pathways more aggressively, leading to a faster approach to the equilibrium ferromagnetic metallic state.

Quantitative analysis employed logarithmic‑linear fitting and non‑linear regression to extract the temperature and field dependence of the decay rate. The decay rate increases with decreasing temperature and increasing magnetic field, consistent with the notion that the kinetic arrest becomes less effective under stronger Zeeman energy and lower thermal agitation. The experimental data were also reproduced by a controlled Markov‑chain model that incorporates state‑dependent transition probabilities, confirming that the observed overtaking can be captured by a simple stochastic framework that encodes the memory of the initial state.

The authors conclude that (1) an overtaking phenomenon analogous to the Mpemba effect exists in solid‑state systems with kinetic arrest; (2) the essential mechanism is the interplay between the initial non‑equilibrium fraction and the energy‑barrier landscape governing relaxation; and (3) this mechanism is generic and may apply to other complex materials such as spin glasses, relaxor ferroelectrics, and phase‑change alloys. They suggest that future work should explore overtaking in different material families, examine the role of disorder and strain, and develop predictive theoretical models that can guide the design of rapid‑reset memory devices and optimized thermal processing protocols. The study thus provides a concrete, artifact‑free explanation for the Mpemba‑type overtaking and opens new avenues for research on non‑equilibrium thermodynamics in correlated electron systems.