Measurement Is Not Free: The Energy Ledger of a Measure-Record-Erase Cycle at the Thermodynamic Floor and in Practice

The standard Szilard-Bennett accounting holds that measurement can in principle be free and that the unavoidable cost of an information cycle sits in erasing the record, at the Landauer floor k_B T ln 2 per bit. This paper tests that accounting for a stated measurement chain. The minimum energy to acquire one bit at error probability p_e against thermal noise is derived for a thermal-noise-limited sampler as E = 2 k_B T [Q^-1(p_e)]^2; at p_e = 1e-6 and 300 K this is 1.87e-19 J per bit, 65.20 times the Landauer floor, and acquisition exceeds erasure at the floor for every error probability below 0.2780. A Texas Instruments ADS1115 converter (16-bit, 860 SPS, 150 microA, datasheet SBAS444E) spends 3.60e-8 J per measured bit in practice. With published DRAM and NAND per-bit energies, the full measure-record-erase cycle costs 1.90e-19 J at the floor (98.49% acquisition) and 3.60e-8 J in practice with a volatile record (99.89% acquisition). The standard claim fails in the stated regime, at the floor and in practice. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).