For fifty years Landauer's principle was a thought experiment. The double-well, the tilting potential, the slow squeeze that sheds kT \ln 2 — all of it lived on blackboards, unfalsified and, to some sceptics, unfalsifiable. Then, beginning in 2012, physicists did something wonderful: they built the double well for real, erased a single bit inside it, and weighed the heat. The number that came out was kT \ln 2. This lesson is the story of those measurements — how you even detect a few zeptojoules, and what "approaching the bound" actually looks like when you plot it.

Bérut 2012: the double well made real

The landmark experiment (Bérut and colleagues, Nature 2012) is the double-well lesson come to life. A single colloidal silica bead, a couple of micrometres across, floats in water inside a double-well optical trap — two focused laser spots making two valleys, with a barrier between them. The bead sitting in the left well is a "0"; in the right well, a "1".

To erase, the experimenters ran exactly the protocol we derived: lower the barrier (dim the trap so the bead can wander both wells), tilt (tip the whole apparatus so a gentle force nudges the bead into one chosen well), then restore the barrier. Whatever well the bead began in, it ends in the target well — a genuine two-states-into-one erasure. And the heat? You cannot put a thermometer on one bead. Instead they filmed the bead's jittery path thousands of times and used the mathematics of stochastic thermodynamics: the work done on the bead is an integral of the trapping force along its recorded trajectory, and averaging over thousands of erasures gives the mean dissipated heat. As the protocol was slowed down, that average slid down towards — and never below — kT \ln 2.

What "approaching the bound" looks like

The signature result is not a single dot at kT \ln 2; it is a curve. Erase quickly and you dissipate a lot; erase slowly and you dissipate less, with the excess above the floor shrinking roughly as one over the protocol duration:

where \tau is how long the erasure takes and c a constant set by the friction. The finite-time surcharge c/\tau is the friction premium the double-well lesson warned about; only in the quasistatic limit \tau \to \infty does it vanish and the heat reach the floor. Drag the slider to change the protocol's friction and watch the curve press down towards the dashed line — but never through it.

This 1/\tau tail is itself a prediction, and matching it — not merely grazing the floor once — is what convinced people the experiment was really seeing Landauer's bound rather than a coincidence.

A whole family of confirmations

Bérut's bead was the first, not the last. The bound has now been hit in wildly different hardware, which is exactly what you want for a claim that is supposed to be technology-independent:

• Jun, Gavrilov & Bechhoefer (2014) — a cleaner feedback optical trap, virtual double-well shaped in real time, measuring the erasure cost with markedly smaller error bars and again converging on kT \ln 2.
• Hong et al. (2016) — erasure of a nanomagnetic bit (a tiny magnetic island, the stuff of hard disks), dissipating about kT \ln 2 — a solid magnet, not a floating bead.
• Single atoms and ions, and superconducting circuits — later experiments pushed the same measurement into quantum-scale hardware, confirming that the floor is not an artefact of soft, watery colloids.

And then there is the converse. If erasing information costs work, then acquiring information ought to let you extract it — the very trade the Szilard engine promised. Toyabe and colleagues (2010) built an information engine: a microscopic particle on a spiral staircase of potential, ratcheted upward against gravity purely by measuring which way it happened to jiggle and clamping a barrier behind it. No force pushed it up; information did. Szilard, vindicated at last in the lab — the demon and its exorcism, both made real.

The theorem that makes it rigorous

How can a single bead sometimes dissipate less than the bound, yet the bound still hold? Because Landauer's kT \ln 2 is a statement about the average over many repeats, and the modern tools that connect single jittery runs to that average are the fluctuation theorems. Jarzynski's equality and the Crooks relation say, in one line, that the exponential average of the work over all the noisy single-shot trajectories equals a clean thermodynamic quantity — so while any one erasure can fluctuate below the floor, the ensemble is pinned above it. These relations are precisely what let Bérut and the others extract a rigorous bound from thousands of noisy little movies.