We have been talking about bits as abstract 0s and 1s. But a bit in a real machine is a physical thing: a dab of charge, a patch of magnetisation, a voltage held on a wire. Before we can put a price on erasing a bit, we need an honest physical picture of what storing one involves. The picture physicists reach for — the one Rolf Landauer used — is beautifully simple: a bit is a ball resting in one of two valleys.

The double-well potential

Imagine a landscape with two dips separated by a hill, described by an energy curve U(x) — a double-well potential, such as

where the parameter b controls the height of the central hill (the barrier). A particle settles into one valley or the other: left valley = 0, right valley = 1. That's a memory. Every real storage technology is a dressed-up version of this — in a flash cell the "particle" is a packet of electrons and the barrier is an insulating oxide layer; on a hard disk the two valleys are two directions of magnetisation.

Play with the landscape below. Drag the barrier down and watch the two valleys merge into one — with no hill between the states, the memory ceases to be a memory. Tilt the landscape and one valley becomes preferred.

What keeps a bit a bit

The particle is not sitting still. At temperature T it is jiggling, constantly kicked by thermal noise with characteristic energy kT (about 25\ \mathrm{meV}, i.e. 4 \times 10^{-21} joules, at room temperature). Following the Boltzmann distribution, the chance of a kick big enough to carry it over a barrier of height \Delta U is suppressed by the famous exponential factor

This factor is ferociously effective. A barrier of just 1\,kT is hopped constantly — useless as a memory. At 40\,kT (about 1 electron-volt), the suppression is e^{-40} \approx 10^{-17}, and a particle rattling against the barrier a billion times a second still waits years to escape. Flash memory hides its electrons behind an oxide barrier of roughly 3\ \mathrm{eV} \approx 120\,kT — which is why your photos survive a decade in a drawer with no power at all.

So a good bit needs a barrier of many kT: stability is bought with energy scale. Note what the barrier does not cost: while the particle just sits in its valley, no energy is being spent. Storing information is free. It is changing the landscape that can cost — and that is where erasure comes in.

Erasure: squeezing two valleys into one

To erase a bit means: whatever valley the particle is in now, end with it in the left valley (a known standard state, "reset to 0"). You are not allowed to look first — erasure must work blind, by manipulating the landscape alone. The classic protocol has three moves, and you can drive it with the slider below:

• lower the barrier — the hill sinks and the two valleys merge into one broad basin; the particle, wherever it started, now wanders the whole basin;
• tilt — raise the right side, and the particle drifts obediently into the left half;
• restore the barrier — the hill rises again, trapping the particle in the left valley. Level the tilt, and the landscape looks exactly as it began.

The landscape ends exactly where it started — but something irreversible has happened. Before, the particle could have been in either valley: two possible states. After, it is in the left valley: one state. The protocol squeezed two possibilities into one — precisely the many-to-one merge that the previous lesson warned about, now happening in a physical energy landscape. Run the film backwards and it makes no sense: the reversed protocol would have to know which valley to return the particle to, and that information no longer exists anywhere in the machine. Its escape route — and the heat that escorts it out — is the subject of the coming lessons.