Hot cools first: the quantum Mpemba effect without bath engineering ✛
Two travelers head for the same destination. One starts closer but takes a winding country road. The other starts farther away but immediately hits the highway. The second arrives first. In quantum physics, this paradox is known as the quantum Mpemba effect: a state initially farther from equilibrium reaches it faster than one that starts closer. For a long time, it was only observed in systems where relaxation channels were artificially engineered, like specially laid-out tracks. Now physicists have shown that the effect arises on its own, in the natural thermal relaxation of nuclear spins in a liquid.
The experiment was performed on a two-spin system of protons in a molecule of 2-chloroacrylonitrile dissolved in dimethyl sulfoxide, using a 500 MHz NMR spectrometer at room temperature. The dominant relaxation mechanism is the dipolar interaction between nuclear spins, that is, energy exchange through magnetic dipoles. This process is described by the GKSL equation with a Liouvillian that has a block structure sometimes called Redfield's "kite." The authors theoretically derived that under certain conditions, the population dynamics reduces to independent relaxation of two qubits with different effective bath temperatures. They then prepared two initial states: one closer to thermal equilibrium, the other farther away but with zero overlap with the slowest decay mode. After preparation, the states were left to evolve without external pulses for up to 29 seconds, which is significantly longer than the longitudinal relaxation time T1 = 5.7 s. Relaxation was monitored by measuring the trace distance to the thermal state.
The result was clear: the state initially farther from equilibrium ($ρ_f$) reaches the thermal state faster than the closer one ($ρ_n$). For parameters θ = 70° and 60°, the distance curves cross, showing the Mpemba effect. Measurements of overlaps with decay modes showed that $ρ_n$ overlaps with both the slow (λ1) and fast (λ3) modes, whereas $ρ_f$ overlaps only with the fast mode. This explains the speedup: $ρ_f$ decays through the fast channel, bypassing the slow one. Furthermore, a "genuine quantum Mpemba effect" was demonstrated: a state with higher free energy ($ρ_f$) reaches equilibrium faster than a state with lower free energy ($ρ_n$). Theoretical predictions agree with the data for a bath correlation time $τ_c$ = 2.1 ps and a dipolar coupling constant b = 5.903 kHz.
The work shows that the quantum Mpemba effect is not an artifact of specially constructed systems but a natural phenomenon that occurs in ordinary thermal relaxation. Understanding the conditions for its occurrence opens the way to harnessing this phenomenon. One can look for similar effects in more complex spin systems, including solid-state qubits, where relaxation is often a limiting factor. It may be possible to develop methods for accelerated initialization of quantum states using natural relaxation channels without additional control. For quantum technologies, this means reduced downtime between computational cycles. For fundamental nonequilibrium statistical mechanics, it refines the limits of validity of Markovian descriptions. The distant traveler who chose the highway is now not just a metaphor but an engineering principle.
The classical Mpemba effect is named after Tanzanian schoolboy Erasto Mpemba, who in 1963 noticed that hot ice cream freezes faster than cold. His observation was long dismissed as an experimental error, but now the effect has a rigorous quantum generalization.
In Kurt Vonnegut's novel 'Cat's Cradle', there is ice-nine, which makes water freeze at room temperature. The Mpemba effect is a milder but real version of paradoxical water behavior, only in the quantum world.