A classical bit is stored as which well of a double well a particle sits in. Erasing the bit means forcing it into a known state (say "0") regardless of where it started — this necessarily discards one bit of information, so Landauer's principle sets a hard lower bound on the heat that must be dissipated:
U(x) = U_b·(x² − 1)² − F(t)·x (double well, tilt F, k_B = 1)
dx = [−∂U/∂x]·dt + √(2·T·dt)·ξ(t) (overdamped Langevin, γ = 1)
W = Σ [U(x_i, λ_{i+1}) − U(x_i, λ_i)] (Sekimoto work: control moves, particle doesn't)
Landauer bound: W_min = k_B·T·ln2
The erase protocol runs in four quarter-duration phases: (1) the barrier is lowered toward a shallow residual well, letting the particle move nearly freely; (2) a tilting force ramps up, biasing it toward the target; (3) — critically — the barrier is rebuilt while the tilt is still fully on, so the particle is trapped on the correct side before anything is relaxed; (4) the tilt is then removed with the bit already locked in. Reforming the barrier before releasing the bias (rather than doing both at once) is what keeps the erasure reliable even for a slow, quasi-static protocol — releasing the bias first lets thermal noise randomize the outcome again before the well reforms.
- Slow erasure (large τ) — near-reversible; measured work approaches the kBT ln2 bound and efficiency climbs.
- Fast erasure (small τ) — the particle can't equilibrate with the changing potential, so extra work is dissipated as heat; efficiency drops well below 100%.
- Run 150 trials tallies work over an ensemble starting from an unknown (randomized) initial bit and draws a live histogram; the mean is verified numerically to sit at or above the bound.
- τ sweep repeats that batch at several erasure durations and plots mean efficiency against τ — the trace climbs toward 100% as the protocol slows down, the signature of approaching the reversible, quasi-static limit.
This is the thought experiment behind the 2012 Bérut et al. colloidal-particle experiment that first measured Landauer's bound directly, and it is why irreversible logic gates in real computer chips have a fundamental (if currently distant) minimum energy cost per bit erased.