Finite memory · equal mass · no free erasure
The Demon's Ledger
Make the right chamber hotter and the left colder. Hold the central wheel only for fast particles travelling right or slow particles travelling left. Every approach writes the gate state into six bits. When the tape fills, the gate locks; erasing it heats the same gas you sorted.
The run is already moving. Hold the wheel, Space, or touch for a precise opening. B releases a higher-throughput burst. E erases only when all six decisions are recorded. Win when a right-hot gradient survives 2.6 seconds after a complete erase; lose by overheating, draining a chamber, or reaching 72 seconds. The first particle is approaching the ledger.