The Cost of Remembering

  • Luca GammaitoniEmail author
  • Igor Neri
  • Miquel López-Suárez
  • Davide Chiuchiù
  • Maria Cristina Diamantini
Conference paper
Part of the Understanding Complex Systems book series (UCS)


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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Luca Gammaitoni
    • 1
    Email author
  • Igor Neri
    • 1
  • Miquel López-Suárez
    • 2
  • Davide Chiuchiù
    • 3
  • Maria Cristina Diamantini
    • 4
  1. 1.Dipartimento di Fisica e Geologia, NiPS LaboratoryUniversità degli studi di PerugiaPerugiaItaly
  2. 2.Institut de Ciència de Materials de Barcelona (ICMAB-CSIC)Bellaterra (Barcelona)Spain
  3. 3.Okinawa Institute for Science and TechnologyOkinawaJapan
  4. 4.Dipartimento di Fisica e Geologia and INFN, NiPS LaboratoryUniversità degli studi di Perugia, Sezione di PerugiaPerugiaItaly

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