The Mpemba effect — hot water freezing faster than cold — has resisted clean explanation for decades. Zheng and Lu (arXiv 2604.01543) now show that the effect’s existence in a double-well potential system depends entirely on a single feature: a reflecting wall. Not the shape of the potential. Not the depth of the wells. Not the asymmetry of the energy landscape. A hard boundary at finite distance from the metastable basin is necessary and sufficient. Remove the wall, and the Mpemba effect vanishes regardless of what the potential looks like. Add the wall, and the counterintuitive dynamics emerge — the system initialized far from equilibrium (the “hot” state) relaxes faster than the one initialized nearby (the “cold” state). The wall creates a return current that accelerates relaxation from the far side while leaving near-side dynamics unchanged.

The Strait of Hormuz operates as a wall condition in geopolitics. The US-Iran escalation — a fighter jet shot down over Iranian airspace on April 3 — is routinely analyzed through strategic gradients: nuclear ambitions, oil access, regional alliances. But the dynamics are driven by the strait’s 21-mile-wide chokepoint, through which 20% of global oil transits daily. Close it, and economic pressure forces military responses regardless of whether the underlying strategic calculus favors restraint. The boundary condition — not the strategic potential landscape — determines what moves. Iran doesn’t need to win a military engagement. It needs to hold the wall. The US doesn’t need to occupy territory. It needs to keep the wall open. Every escalatory step since February 28 has been geometrically constrained to the strait and its approaches, because that is where the constraint binds.

The parallel is structural, not metaphorical. In the Mpemba system, the double-well shape determines what the equilibrium looks like, but the wall determines how fast — and from which direction — the system gets there. In the Hormuz system, the strategic objectives determine what the end state looks like, but the geographic constraint determines the path of escalation.

In both systems, the constraint creates the dynamics, not the gradient.