The Observation Boundary: Landauer at Every Measurement

Synthesis. The leakage form across three domains has the same shape: k_B × T × O(1) per erased bit. Three boundaries, one thermodynamic cost.

4.1 — The Landauer principle

Landauer (1961) proved: erasing one bit of information requires minimum energy dissipation:

E_min = k_B T ln 2 (4.1)

This is a theorem of statistical mechanics, experimentally verified [Bérut et al. 2012].

4.2 — Measurement as observation

Every quantum measurement extracts information. Between measurements, unitary evolution preserves information. At the measurement event, three things happen simultaneously: (a) decoherence relative to the measurement basis; (b) information extraction (a definite outcome is recorded); (c) any logically irreversible erasure or reset of the recorded outcome dissipates at minimum k_B T ln 2 per erased bit. The leakage is therefore the thermodynamic cost of maintaining an observation record over time, not a mandatory dissipation at the instant of measurement.

4.3 — Three channels, one form

Claim C4 (Synthesis). The leakage cost per bit has the same form in all three domains: E_leak/bit = k_B × T × O(1), where T is set by the boundary physics and O(1) is a constant of order unity. Gravitational: k_B T_H. Electromagnetic: k_B T_body ln 2. Cosmological: k_B T_CMB.

4.4 — Honest qualification

The form of the leakage cost per bit (k_B T) is constant across domains. The ratio of leakage to total incoming energy is not constant — it depends on specific temperatures and coupling constants differing by many orders of magnitude. The structural isomorphism is in the form, not the magnitude.