The Izumi--Szilard Engine: Separating Information Erasure from Mechanical Work Extraction

Abstract

The conventional Szilard engine combines a one-molecule expansion withmeasurement, memory, and feedback. The ideal isothermal expansion work andthe Landauer bound for resetting an unbiased binary memory both contain thequantity \(k_{\mathrm B}T\ln 2\), but they refer to distinct physicalprocesses. We introduce the Izumi--Szilard engine to separate informationerasure from mechanical work extraction. In the proposed architecture, a symmetric mechanical coupling allowsmolecular expansion in either direction to raise the same load,\[U_L(+x_s)=U_L(-x_s).\]No molecular-side measurement, separately stored binary record, ormeasurement-conditioned branch protocol is required. Although the sign ofthe piston displacement can be assigned a binary label, that label is carriedby the same piston--load coordinate that stores mechanical energy and is notan additional thermodynamic subsystem. Consequently, no independentLandauer-reset term should be added unless a distinct information-bearingdegree of freedom is physically prepared and reset. This conclusion does not establish positive net work. The complete cyclemust include the signed work of partition insertion and removal, finite-masspiston fluctuations, load and coupling dynamics, actuator and timing work,reverse transitions, and restoration of every internal component. For afinite-thickness partition, insertion and removal works cancel only when theyform an exact reversible reverse pair. More generally, we propose a pairedtwo-engine mechanism in which insertion in one engine coincides with removalin the other, allowing the recoverable components of partition work to beexchanged internally. In the symmetric, thin-partition, synchronized limit,only residual mismatch and dissipative losses remain as external partitioncosts. The relevant output is the work ultimately delivered to an externalrepository, not the intermediate work used to raise the load. We thereforeformulate a signed mechanical work balance and require complete statisticalcycle closure of the engine and all auxiliary mechanisms. We also propose acalorimetric test in which the stored mechanical work is delivered to athermally isolated body initially hotter than the working reservoir. Excessheating of that body would verify the previously extracted mechanical workafter its conversion into heat. If a complete autonomous cycle returns all internal and auxiliary degrees offreedom to their initial statistical states while producing persistentexternal free-energy gain, the result would directly test theKelvin--Planck statement. Otherwise, the failure should be attributed to anidentified mechanical or dynamical compensation mechanism rather than toinformation erasure as a generic explanation.