Landauer's Bit-Erasure Engine: Minimum Energy Cost of Deleting Information

Bit State

?current bit

Erasure Protocol

Erase to 0

Erasure duration τ 1.5 s

Barrier height U_b 2.5 kT

Temperature T 1.00

Measured Thermodynamics

Work, this run

— kT

Landauer bound

— kT

Efficiency (bound ⁄ work)

—

Runs completed · avg efficiency

0 runs

How it works

A classical bit is stored as which well of a symmetric 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)
dx = [−dU/dx]·dt + √(2·T·dt)·ξ(t)  (overdamped Langevin, γ=1, k_B=1)
W = Σ [U(x_i, λ_{i+1}) − U(x_i, λ_i)]   (work = energy change from moving the *controls*, not the particle)
Landauer bound:  W_min = k_B·T·ln2

The erase protocol runs in three phases over the chosen duration τ: (1) the barrier U_b is lowered to 0, letting the particle move freely; (2) a tilting force F is ramped up, biasing the particle toward the target well; (3) the barrier is raised again while the tilt is removed, trapping the particle in the target state. Every joule spent tilting and re-shaping the well is tallied as work.

Slow erasure (large τ) — near-reversible; measured work approaches the k_BT ln2 bound and efficiency climbs toward 100%.
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%.
Higher barrier / higher temperature — a taller barrier needs a stronger, costlier tilt to overcome; higher T raises both the noise floor and the bound itself (proportionally).
Between runs the bit isn't fixed — thermal noise can flip it over the barrier on its own, which is why the bit reads "?" whenever the particle sits near the top.

This is the exact thought experiment behind the 2012 Bérut et al. colloidal-particle experiment that first measured Landauer's bound directly, and it is the reason irreversible logic gates in real computer chips have a fundamental (if currently distant) minimum energy cost per bit erased.

Idle

Particle (the bit) Double-well potential

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