Hot water sometimes freezes faster than cold. Ice forms more quickly from boiling water. This paradox, discovered by schoolboy Erasto Mpemba, long puzzled physicists. It turns out: the farther a system is from equilibrium, the faster it relaxes back to it.
A similar paradox has been found inside living cells. It is demonstrated by the walking protein kinesin — a molecular courier. It steps along microtubules, delivering vital cargo. Each step, 8 nanometers long, burns one molecule of ATP — the cell's fuel.
Researchers built a six-state model of the motor. They tested its behavior with and without fuel. Even at rest, Stochastic modeling obeys the Mpemba effect: starting from a “hot” state speeds up the transition to a steady walking rhythm. The secret lies in how entropy (a measure of disorder) changes along the path to equilibrium. From chaos, the system finds the main road to calm faster. Adding fuel or load didn't break the pattern — they merely shifted the conditions for the speedup. Interestingly, the walking speed itself betrays the anomaly. It can be measured in the lab.
So, in the nanoworld, the shortest path isn't always the quickest. A motor that starts farther away often reaches its goal sooner — just as hot water turns to ice faster than cold.
as written by the authors arXiv:2607.27998v1
The Mpemba effect, wherein a system prepared farther from equilibrium relaxes faster than one initially closer to equilibrium, has been extensively investigated in a wide range of physical systems. In contrast, its role in biologically relevant non-equilibrium processes remains largely unexplored. Here, we investigate anomalous relaxation in the six-state chemomechanical network model of the Kinesin molecular motor under both equilibrium and non-equilibrium conditions. We first establish the existence of the Mpemba effect in chemical equilibrium and show that many of its qualitative features can be understood from the underlying free-energy landscape. We then examine the effects of mechanical and chemical driving, showing that breaking detailed balance primarily reshapes the Mpemba phase diagram without qualitatively altering the relaxation phenomenology over the physically relevant parameter regime. Finally, we demonstrate that the relaxation of the motor velocity also mirrors the anomalous relaxation of the underlying stochastic dynamics, thereby identifying an experimentally accessible signature of the Mpemba effect. Our results establish molecular motors as a promising baseline for studying anomalous relaxation in living systems and suggest a broader framework for exploring the Mpemba effect in non-equilibrium biochemical networks.
Kinesin's step is 8 nanometers. That distance is enough to keep it on track: the microtubule is marked like a trail with repeating protein blocks.