The Cost of Remembering
In 1961, Rolf Landauer pointed out that resetting a binary memory requires a minimum energy of \(k_BT ln(2)\). However, once written, any memory is doomed to loose its content if no action is taken. To avoid memory losses, a refresh procedure is periodically performed. In this work we present a theoretical and experimental study of sub-\(k_BT\) system to evaluate the minimum energy required to preserve one bit of information over time. Two main conclusions are drawn: (i) in principle the energetic cost to preserve information for a fixed time duration with a given error probability can be arbitrarily reduced if the refresh procedure is performed often enough; (ii) the Heisenberg uncertainty principle sets an upper bound on the memory lifetime, thus no memory can last forever.
The authors gratefully acknowledge financial support from the European Commission (H2020, Grant agreement no: 732631, OPRECOMP, FPVII, Grant agreement no: 318287, LANDAUER and Grant agreement no: 611004, ICT- Energy) and ONRG grant N00014-11-1-0695.
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