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Landauer's erasure principle states that any irreversible erasure protocol ofa single bit memory needs work of at least $k_B T ln2.$ Recent proof of conceptexperiments has demonstrated that the erasure protocols with work close to theLandauer limit can be devised. Under feedback, where the state of the bit canbe measured, the work needed for bit erasure can be lower than $k_B T ln2.$ Inthis article, we analyze the energetics of feedback enabled erasure, whileincorporating the imperfections of experimentally realized memory and biterasure protocols that admit failure probabilities. We delineate the role ofuncertainty in measurements and its effects on the work and entropy changes fora feedback-based erasure. We quantitatively demonstrate that the deficitbetween the Landauer limit and the minimum average work needed in afeedback-based erasure is accounted for by the mutual information between themeasurement and the state of the memory, while incorporating the imperfectionsinherent in any realization. We experimentally demonstrate analysis results ona memory and erasure protocol realized using optical fields.

Energetics of Feedback: Application to Memory Erasure