This article analyzes the effect of imperfections in physically realizable memory. Motivated by the realization of a bit as a Brownian particle within a double well potential, we investigate the energetics of an erasure protocol under a Gaussian mixture model. We obtain sharp quantitative entropy bounds that not only give rigorous justification for heuristics utilized in prior works, but also provide a guide toward the minimal scale at which an erasure protocol can be performed. We also compare the results obtained with the mean escape times from double wells to ensure reliability of the memory. The article quantifies the effect of overlap of two Gaussians on the the loss of interpretability of the state of a one bit memory, the required heat dissipated in partially successful erasures and reliability of information stored in a memory bit.
Bibliographical noteFunding Information:
Author Contributions: S.T. and S.B. conceptualized the problem and wrote the manuscript. S.T., S.B. and J.M. worked on the analytical aspects. M.S. has provided numerous insights through discussions. J.M. and M.S. were involved in reviewing and editing of the manuscript. M.S. has led the project and is the principal investigator (PI) of the National Science Foundation (NSF) grants supporting this research.
Funding: The authors acknowledge the support of the National Science Foundation for funding the research under Grant No. CMMI-1462862 and ECCS 1809194.
- Generalized Landauer's principle
- Information erasure
- Reliability of a bit
- Thermodynamics of information