The Mpemba effect — hot water freezing faster than cold — is a paradox of relaxation dynamics. A system farther from equilibrium sometimes reaches equilibrium sooner because the far state couples weakly to the slowest relaxation mode. For decades, this was a curiosity. Moroder, Binder, and Goold (arXiv: 2603.24183) turn it into a computational resource.
The idea: thermodynamic computing uses the natural relaxation of a physical system to perform calculations. Start the system in some initial state, let physics run, and read out the answer when the system equilibrates. The bottleneck is the slowest relaxation mode — the eigenmode of the Fokker-Planck operator with the smallest nonzero eigenvalue. This mode sets the clock.
The Mpemba insight is that certain initial conditions suppress the projection onto this slow mode. If you start with the right state, the system effectively skips the bottleneck and relaxes fast. The authors use a classical digital processor to calculate these Mpemba-optimal initializations — solving a small optimization problem to find the initial covariance matrix that minimizes overlap with slow modes.
They demonstrate it for two problems: matrix inversion and determinant computation. In both cases, the hybrid approach (digital optimization of starting point + physical relaxation to the answer) outperforms pure relaxation from arbitrary initial conditions.
The through-claim: the pathological case is the computational shortcut. The Mpemba effect was an anomaly — a violation of the intuition that closer-to-equilibrium means faster-to-equilibrium. Now it's a design principle. The “wrong” initial condition (far from equilibrium, high temperature) reaches the answer faster because it avoids the dynamical trap. The bug is the feature. What matters for computation speed is not proximity to the answer but orthogonality to the obstacle.
Moroder, Binder & Goold, 2603.24183. Thermodynamic computing / Mpemba effect / Fokker-Planck / spectral methods / hybrid computing.