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Thermodynamics of computation and linear stability limits of superfluid refrigeration of a model computing array

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Abstract

We analyze the stability of the temperature profile of an array of computing nanodevices refrigerated by flowing superfluid helium, under variations in temperature, computing rate, and barycentric velocity of helium. It turns out that if the variation in dissipated energy per bit with respect to temperature variations is higher than some critical values, proportional to the effective thermal conductivity of the array, then the steady-state temperature profiles become unstable and refrigeration efficiency is lost. Furthermore, a restriction on the maximum rate of variation in the local computation rate is found.

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Acknowledgements

This work was supported by National Group of Mathematical Physics (GNFM-INdAM). LG is supported by the Engineering and Physical Sciences Research Councile (EPSRC), Grant EP/R005192/1. D.J. acknowledges the financial support from the Dirección General de Investigación of the Spanish Ministry of Economy and Competitiveness under Grant TEC2015-67462-C2-2-R and of the Direcció General de Recerca of the Generalitat of Catalonia, under Grant 2017 SGR-1018, and to Consolider Program Nanotherm (Grant CSD-2010-00044) of the Spanish ministry of Science and Innovation. The authors would thank the anonymous referee for his help to improve our paper.

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Authors and Affiliations

  1. Dipartimento di Scienze Agrarie, Alimentari e Forestali, Università di Palermo, Viale delle Scienze, 90128, Palermo, Italy

    Michele Sciacca

  2. Dipartimento di Ingegneria Industriale, Università di Salerno, Campus di Fisciano, 84084, Fisciano, Italy

    Antonio Sellitto

  3. Joint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

    Luca Galantucci

  4. Departament de Física, Universitat Autònoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    David Jou

  5. Institut d’Estudis Catalans, Carme 47, 08001, Barcelona, Catalonia, Spain

    David Jou

Authors
  1. Michele Sciacca
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  2. Antonio Sellitto
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  3. Luca Galantucci
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  4. David Jou
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Correspondence to Michele Sciacca.

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Sciacca, M., Sellitto, A., Galantucci, L. et al. Thermodynamics of computation and linear stability limits of superfluid refrigeration of a model computing array. Z. Angew. Math. Phys. 70, 121 (2019). https://doi.org/10.1007/s00033-019-1162-7

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  • DOI: https://doi.org/10.1007/s00033-019-1162-7

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