Landauer's Principle and the Thermodynamic Cost of Computation

Abstract

Landauer's principle sets a fundamental lower bound of k_BT ln2 on the heat dissipated per irreversibly erased bit,
yet the degree to which real computational hardware approaches this bound during sustained, high-speed
operation, rather than in slow, quasi-static demonstrations, has remained only partially characterized. We measured
energy dissipation per bit erasure in a single-electron double-well memory device operated across 45 combinations
of erasure protocol duration (10 microseconds to 10 milliseconds) and bath temperature (250-320 K), comparing
measured dissipation to the Landauer bound of k_BT ln2 computed at each operating temperature. At the slowest
erasure protocol tested (10 ms) and a bath temperature of 300 K, measured dissipation was 1.18 times the
Landauer bound (3.44 x 10^-21 J versus a bound of 2.87 x 10^-21 J), the closest approach to the theoretical limit
observed across all conditions tested. Reducing erasure duration to 10 microseconds increased measured
dissipation to 6.9 times the Landauer bound at the same bath temperature, a 485% relative excess, consistent with
the expected 1/tau scaling of excess dissipation predicted by finite-time information-erasure theory. Across the full
45-condition matrix, excess dissipation above the Landauer bound correlated with protocol duration with a fitted
power-law exponent of -0.94 (95% CI: -1.02 to -0.87, R2 = 0.91), closely consistent with the theoretically predicted
inverse scaling. Bath temperature had a comparatively modest independent effect: at fixed erasure duration (1 ms),
raising bath temperature from 250 K to 320 K increased the absolute Landauer bound by 28% as expected, but the
dissipation-to-bound ratio changed by less than 6% across this temperature range, indicating that the relative
approach to the fundamental limit was largely temperature-independent over the range tested. A control series
using a symmetric, logically reversible double-well protocol (no net bit erasure) showed dissipation consistent with
zero net Landauer cost within measurement uncertainty at all tested durations, confirming that the measured
dissipation in the erasure protocols was specifically attributable to the irreversible bit-erasure operation rather than
to parasitic dissipation in the device or measurement chain. These results provide a quantitative erasure-duration
map for approaching the Landauer limit in a physical memory device and establish protocol duration, rather than
operating temperature, as the dominant lever for minimizing the thermodynamic cost of computation in this device
class.