Phase Transition in Protocols Minimizing Work Fluctuations

Physical Review Letters
Alexandre P Solon, Jordan M Horowitz

Abstract

For two canonical examples of driven mesoscopic systems-a harmonically trapped Brownian particle and a quantum dot-we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal-work protocols, which therefore never become quasistatic.

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Citations

Feb 6, 2019·Physical Review Letters·Alexandre G R DayDries Sels
Jul 25, 2019·Physical Review. E·Domingos S P Salazar, Sérgio A Lira
Apr 4, 2020·Physical Review Letters·Deepak GuptaArnab Pal
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Feb 15, 2020·Physical Review Letters·Kay Brandner, Keiji Saito
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Feb 20, 2019·Physical Review. E·Carlos A PlataA Prados
Oct 21, 2020·Physical Review. E·Karel ProesmansJohn Bechhoefer
Jan 16, 2021·Physical Review Letters·Harry J D Miller, Mohammad Mehboudi
Jan 1, 2021·The Journal of Chemical Physics·Steven Blaber, David A Sivak
May 12, 2021·Proceedings of the National Academy of Sciences of the United States of America·Tushar K SahaJohn Bechhoefer
Aug 15, 2019·Chemical Reviews·Aidan I Brown, David A Sivak

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