- Physical Review Journals
All JournalsPhysics Magazine

PRX Energy

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Optimal Control of Bit Erasure in Stochastic Random Access Memory

Songela W. Chen1,2 and David T. Limmer1,2,3,4,*

  • *Contact author: dlimmer@berkeley.edu
PDF

PRX Energy 5, 023011 – Published 16 June, 2026

DOI: https://doi.org/10.1103/bmsv-mlq5

Abstract

Energy costs of information processing are growing exponentially. Bit erasure is a key problem in this energy-information nexus, and a number of seminal relationships have been deduced regarding the relationship between thermodynamic costs and memory storage. To continue making progress in the modern era, however, requires confronting thermodynamic costs in realistic physical systems, which operate away from equilibrium. Here, we explore the thermodynamic costs of bit erasure in a complementary metal-oxide-semiconductor model of two types of random-access memory. We find dynamic random-access memory dissipates the least amount of energy when operated in the quasistatic limit, where errors are also minimized. By contrast, static random-access memory is most efficiently operated in finite time due to the energy required to maintain the state of the bit. We demonstrate a numerically robust optimization scheme using mean field theory and automatic differentiation, finding optimal protocols compatible with electrical engineering insights. These results provide a framework for operating realistic circuits in thermodynamically advantageous ways.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

This work bridges microscopic physics with practical engineering concerns for operating computer chips. Energy costs of information technology have grown exponentially. To continue making computers more efficient as chips become smaller, we must confront thermodynamic costs of nanoscale physical systems that have random noise. In this paper, the authors explore the energy costs of erasing bits of information in two realistic models of memory based on modern computer architectures. Information stored in dynamic random access memory is most efficiently erased when accomplished over a long operating time, as slower operations release less heat. In contrast, static random access memory has an ongoing cost to keep its information stored reliably, so erasure is most efficient when done quickly. The authors use machine-learning-based techniques to find optimal protocols that are consistent with electrical engineering insights. These results provide a framework for operating realistic circuits in energetically advantageous ways.

Article Text

References (40)

  1. International Energy Agency, Energy and AI, Tech. Rep. (International Energy Agency, 2025).
  2. R. Landauer, Irreversibility and heat generation in the computing process, IBM J. Res. Dev. 5, 183 (1961).
  3. T. Sagawa and M. Ueda, Minimal energy cost for thermodynamic information processing: Measurement and information erasure, Phys. Rev. Lett. 102, 250602 (2009).
  4. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, Experimental verification of Landauer’s principle linking information and thermodynamics, Nature 483, 187 (2012).
  5. G. W. Wimsatt, A. B. Boyd, P. M. Riechers, and J. P. Crutchfield, Refining Landauer’s stack: Balancing error and dissipation when erasing information, J. Stat. Phys. 183, 16 (2021).
  6. S. Dago, J. Pereda, N. Barros, S. Ciliberto, and L. Bellon, Information and thermodynamics: Fast and precise approach to Landauer’s bound in an underdamped micromechanical oscillator, Phys. Rev. Lett. 126, 170601 (2021).
  7. K. Proesmans, J. Ehrich, and J. Bechhoefer, Optimal finite-time bit erasure under full control, Phys. Rev. E 102, 032105 (2020).
  8. P. R. Zulkowski and M. R. DeWeese, Optimal finite-time erasure of a classical bit, Phys. Rev. E 89, 052140 (2014).
  9. L. T. Giorgini, R. Eichhorn, M. Das, W. Moon, and J. S. Wettlaufer, Thermodynamic cost of erasing information in finite time, Phys. Rev. Res. 5, 023084 (2023).
  10. A. B. Boyd, A. Patra, C. Jarzynski, and J. P. Crutchfield, Shortcuts to thermodynamic computing: The cost of fast and faithful information processing, J. Stat. Phys. 187, 17 (2022).
  11. M. A. Ciampini, T. Wenzl, M. Konopik, G. Thalhammer-Thurner, M. Aspelmeyer, E. Lutz, and N. Kiesel, Erasure of a nonequilibrium memory beyond Landauer’s bound using levitated optomechanics with spatio-temporal optical control, Phys. Rev. Res. 7, 043321 (2025).
  12. S. Dago, S. Ciliberto, and L. Bellon, Reliability and operation cost of underdamped memories during cyclic erasures, Adv. Phys. Res. 3, 2300074 (2024).
  13. Y. Taur and T. H. Ning, Fundamentals of Modern VLSI Devices (Cambridge University Press, Cambridge, United Kingdom; New York, NY, 1998).
  14. J. Koomey, S. Berard, M. Sanchez, and H. Wong, Implications of historical trends in the electrical efficiency of computing, IEEE Ann. Hist. Comput. 33, 46 (2011).
  15. C. Y. Gao and D. T. Limmer, Principles of low dissipation computing from a stochastic circuit model, Phys. Rev. Res. 3, 033169 (2021).
  16. N. Freitas, J.-C. Delvenne, and M. Esposito, Stochastic thermodynamics of nonlinear electronic circuits: A realistic framework for computing around kT, Phys. Rev. X 11, 031064 (2021).
  17. J. Gu and P. Gaspard, Counting statistics and microreversibility in stochastic models of transistors, J. Stat. Mech: Theory Exp. 2020, 103206 (2020).
  18. L. W. Nagel and D. Pederson, SPICE (Simulation Program with Integrated Circuit Emphasis), Tech. Rep. UCB/ERL M382 (University of California, Berkeley, 1973).
  19. P. Helms, S. W. Chen, and D. T. Limmer, Stochastic thermodynamic bounds on logical circuit operation, Phys. Rev. E 111, 034110 (2025).
  20. N. Freitas, K. Proesmans, and M. Esposito, Reliability and entropy production in nonequilibrium electronic memories, Phys. Rev. E 105, 034107 (2022).
  21. C. Murphy, S. Nicholson, N. Freitas, E. Penocchio, and T. Gingrich, Dissipation-reliability tradeoff for stochastic CMOS bits in series, arXiv:2603.04658 [cond-mat].
  22. T. Shimizu, K. Chida, G. Yamahata, and K. Nishiguchi, Thermodynamic constraints in dynamic random-access memory cells: Experimental verification of energy efficiency limits in information erasure, Phys. Rev. Lett. 136, 117103 (2026).
  23. T. Basile and K. Proesmans, Optimal control of static RAM erasure: Arbitrarily fast operation with finite dissipation, New J. Phys. 27, 104601 (2025).
  24. L. Brillouin, Can the rectifier become a thermodynamical demon? Phys. Rev. 78, 627 (1950).
  25. D. T. Limmer, Statistical Mechanics and Stochastic Thermodynamics (Oxford University Press, Oxford, United Kingdom; New York, NY, 2024).
  26. R. Sarpeshkar, T. Delbruck, and C. A. Mead, White noise in MOS transistors and resistors, IEEE Circuits Devices Mag. 9, 23 (1993).
  27. D. T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys. 22, 403 (1976).
  28. D. T. Gillespie, Stochastic simulation of chemical kinetics, Annu. Rev. Phys. Chem. 58, 35 (2007).
  29. M. Esposito and C. Van den Broeck, Three detailed fluctuation theorems, Phys. Rev. Lett. 104, 090601 (2010).
  30. M. C. Engel, J. A. Smith, and M. P. Brenner, Optimal control of nonequilibrium systems through automatic differentiation, Phys. Rev. X 13, 041032 (2023).
  31. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980 [cs].
  32. J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: composable transformations of Python + NumPy programs, 2018, http://github.com/jax-ml/jax
  33. P. Kidger, On neural differential equations, PhD thesis, University of Oxford, 2021.
  34. S. Whitelam, Nonequilibrium formulation of varying-temperature bit erasure, J. Stat. Mech: Theory Exp. 2024, 063203 (2024).
  35. L. Van Brandt and J.-C. Delvenne, in 2023 IEEE 23rd International Conference on Nanotechnology (NANO) (IEEE, Jeju City, Korea, Republic of, 2023), pp. 726–731.
  36. L. Van Brandt and J.-C. Delvenne, Noise–dissipation relation for nonlinear electronic circuits, Appl. Phys. Lett. 122, 263507 (2023).
  37. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  38. K. Proesmans, J. Ehrich, and J. Bechhoefer, Finite-time Landauer principle, Phys. Rev. Lett. 125, 100602 (2020).
  39. S. W. Chen and D. T. Limmer, Code and data for “Optimal control of bit erasure in stochastic random access memory” (2026), https://doi.org/10.5281/zenodo.19582802
  40. D. A. Sivak and G. E. Crooks, Thermodynamic metrics and optimal paths, Phys. Rev. Lett. 108, 190602 (2012).

Outline

Information

PRX Energy 5, 023011– Published 16 June, 2026
  • Received 27 January 2026
  • Revised 14 April 2026
  • Accepted 14 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation