Abstract
We investigate the performance of majority-logic decoding in both reversible and finite-time information erasure processes performed on macroscopic bits that contain N microscopic binary units. While we show that for reversible erasure protocols single-unit transformations are more efficient than majority-logic decoding, the latter is found to offer several benefits for finite-time erasure processes: Both the minimal erasure duration for a given erasure and the minimal erasure error for a given erasure duration are reduced, if compared to a single unit. Remarkably, the majority-logic decoding is also more efficient in both the small-erasure error and fast-erasure region. These benefits are also preserved under the optimal erasure protocol that minimizes the dissipated heat. Our work therefore shows that majority-logic decoding can lift the precision-speed-efficiency trade-off in information erasure processes.
Highlights
For modern society that is characterized by ubiquitous digitalization, information storage and processing are of utmost importance
We studied the performance of majority-logic decoding in reversible and finite-time information erasure processes
The physical information stored inside the N microscopic units is translated into logical information stored in the macroscopic bit via the majority-logic decoding scheme that can be mathematically formulated via an incomplete regularized beta function
Summary
For modern society that is characterized by ubiquitous digitalization, information storage and processing are of utmost importance. It was, for instance, proven that in the low-dissipation limit the optimal, i.e., the least work-intense, transformation protocol between two sets of probabilities will lead to an irreversible entropy production, i.e., dissipation, that is inversely proportional to the transformation duration [26,27,28] This result has been applied beyond the theory of information processing, e.g., for the study of efficiencies of finite-time heat engines [29,30,31,32,33,34]. √ safety of the information processing is enhanced since the signal-to-noise ratio is proportional to N, where N is the number of microscopic grains contained in a macroscopic bit [35] It is the aim of this paper to extend the existing studies of the thermodynamics of finite-time information erasure processes in single microscopic two-state systems by considering non-interacting ensembles of them under a specific decoding procedure.
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