Deep Field / case

Szilard Engine

One ideal-gas molecule occupies a rigid box bisected by a movable partition at temperature T. A measurement apparatus coupled to a memory register determines left versus right—one bit acquired. The molecule expands isothermally against the partition, extracting work W = kBT ln 2. To cycle again the register must erase, dissipating at minimum Qmin = kBT ln 2 into the heat bath. Work extracted equals minimum erasure cost; the Demon gains nothing net. What is maintained across cycles is apparatus state discipline: discriminate, store, act, reset. Payment is Landauer-floor dissipation per logically irreversible bit erasure—vanishing per bit, unbounded in the Demon's open ledger of total microstate access. Treat measurement or memory as free and the wager revives a standpoint thermodynamically forbidden inside finite-observer physics. Withhold erasure and the engine cannot reset; after erasure is priced, no net work gain remains.