The Thermodynamic Budget of a Never-Erasing Memory: Retention Is Free, Correction Is the Bill

A persistent-memory system that never erases and never resets is worked out thermodynamically, separating retention, writing, and error correction. Indefinite retention has a fundamental cost of exactly zero (storage is not erasure); append-only growth pays the Landauer bound once per new bit for blank-medium preparation; the only recurring fundamental cost is exporting the entropy of spontaneous bit errors at scrubbing. A budget equation for retention time versus error-correction energy is derived (minimum scrubbing power and longest admissible scrub interval in closed form for t-error-correcting codes). For a stated reference system (8e12 bits at 300 K, flip hazard 1e-8 per bit per year, 100-year horizon, failure probability at most 0.01), the fundamental 100-year correction energy is 8.5e-13 J (single-error correction). Minimum power grows only logarithmically with retention horizon: there is no thermodynamic wall against indefinite retention. The practical bill falls on scrubbing input/output and medium choice, roughly 1e18 above the fundamental floor per scrub under an illustrative engineering parameter. All numerical values are model calculations (SIMULATED, NOT MEASURED), produced by the deposited compute.py.