Harnessing fluctuations in thermodynamic computing via time-reversal symmetries

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Harnessing fluctuations in thermodynamic computing via time-reversal symmetries

Gregory Wimsatt, Olli-Pentti Saira, Alexander B. Boyd, Matthew H. Matheny, Siyuan Han, Michael L. Roukes, and James P. Crutchfield

Phys. Rev. Research 3, 033115 – Published 5 August 2021

Abstract

We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of microscopic trajectories. As a consequence, we introduce a broad family of conditional fluctuation theorems that the component work distributions must satisfy. Since they identify entropy production, the component work distributions encode the frequency of various mechanisms of both success and failure during computing, as well giving improved estimates of the total irreversibly dissipated heat. This new diagnostic tool provides strong evidence that thermodynamic computing at the nanoscale can be constructively harnessed. We experimentally verify this functional decomposition and the new class of fluctuation theorems by measuring transitions between flux states in a superconducting circuit.

Received 29 January 2021
Accepted 21 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033115

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

Physics Subject Headings (PhySH)

Entropy Fluctuation theorems Nonequilibrium statistical mechanics Thermodynamics of computation Work theorems

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Gregory Wimsatt^1,*, Olli-Pentti Saira^2,†, Alexander B. Boyd^1,‡, Matthew H. Matheny^2,§, Siyuan Han^3,∥, Michael L. Roukes^2,¶, and James P. Crutchfield ^1,2,#

¹Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
²Condensed Matter Physics and Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
³Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA

^*gwwimsatt@ucdavis.edu
^†osaira@caltech.edu
^‡abboyd@ucdavis.edu
^§matheny@caltech.edu
^∥han@ku.edu
^¶roukes@caltech.edu
^#Corresponding author: chaos@ucdavis.edu

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Vol. 3, Iss. 3 — August - October 2021

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Images

Figure 1
Inner plot sequence: Erasure protocol (Table 1) evolution of position distribution $Pr (x)$ from simulation. Potential $V (x, t_{s})$ at substage boundary times $t_{s}, s = 0, 1, 2, 3, 4$ . Starting at $t = t_{0}$ , the potential evolves clockwise, ending at $t = t_{4}$ in the same configuration as it starts: $V (x, t_{0}) = V (x, t_{4})$ . However, the final position distribution $Pr (x)$ predominantly indicates the $R$ state. The original one bit of information in the distribution at time $t = t_{0}$ has been erased. Outer plot sequence: Substage work distributions from simulation $Pr (W_{s}, C_{s})$ during substages $s$ : (1) Barrier Drop, (2) Tilt, (3) Barrier Raise, (4) Untilt. During each substage $s$ , distributions are given for up to three substage trajectory classes $C_{s}$ : red consists of trajectories always in the $R$ state, orange trajectories always in the $L$ state, and blue the rest, spending some time in each state.
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Figure 2
Rear (purple): total work distribution of all trajectories $Pr (W_{total})$ during erasure simulation: a histogram generated from $3.5 \times 10^{6}$ trials for $W_{total} \in [- 6, 4]$ over 201 bins. Inset (gray): typical unimodal work distribution illustrated for a spatially translated thermally driven simple harmonic oscillator. Three front plots: work distributions $Pr (W_{total}, C_{4})$ for the trajectory classes $C_{4}$ determined by the untilt trajectory partition in simulation: The red work distribution (middle) is that of Success trajectories, the orange (rear) is that of Fail trajectories, and the blue (front) is that of the remaining, Transitional trajectories.
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Figure 3
Superconducting implementation of metastable memory and bit erasure driven by thermal fluctuations: (a) Optical micrograph of a gradiometric flux qubit with control lines and local magnetometers for state readout. The flux $ϕ_{x}$ , threading the large U-shaped differential-mode loop, controls the potential's tilt, and the flux $ϕ_{xdc}$ , threading the small SQUID loop, controls the potential barrier height. Currents in the barrier control and tilt control lines modulate those fluxes. (b) Calculated potential energy landscape at the beginning of the erasure protocol; see Eqs. (J1) and (J2). (c, top) Sequence of tilt and barrier control waveforms implementing bit erasure, and (c, bottom) sample of resulting magnetometer traces tracking the system's internal state. Note that for this experiment, in contrast to the simulation, two possible informational states were present at all times during the protocol. So, though the barrier was reduced sufficiently to allow transitions to the target $R$ state, the trace is attracted to either a positive or negative value at all times. (d) Work distributions $Pr (W_{total} | C_{4})$ over trajectories conditioning on the Success, Fail, and Transitional classes. Experimental distributions obtained from $10^{5}$ protocol repetitions.
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Figure 4
Flux qubit experiment work fluctuations: Crooks' work fluctuation theorem prediction (green dashed line), measured values (blue), and 1- $σ$ statistical errors (red).
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