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  • Open Access

Join gate with memory in token-conserving Brownian circuits and the thermodynamic cost

Yasuhiro Utsumi

  • Department of Electrical and Electronic Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan

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Phys. Rev. E 113, 024129 – Published 19 February, 2026

DOI: https://doi.org/10.1103/pmx1-rz3n

Abstract

The token-based Brownian circuit harnesses the Brownian motion of particles for computation. The conservative join (CJoin) is a circuit element that synchronizes two Brownian particles, and its realization using repelling particles, such as magnetic skyrmions or electrons, is key to building the Brownian circuit. Here, a theoretical implementation of the CJoin using a simple quantum dot circuit is proposed, incorporating an internal state, a double quantum dot that functions as a one-bit memory, storing the direction of two-particle transfer. A periodic reset protocol is introduced, allowing the CJoin to emit particles in a specific direction. The stochastic thermodynamics under periodic resets identifies the thermodynamic cost as the work done for resets minus the entropy reduction due to resets, with its lower bound remaining within a few multiples of kBT at temperature T. Applying the speed limit relation to a subsystem in bipartite dynamics, the number of emitted particles is shown to be relatively tightly bounded from above by an expression involving the subsystem's irreversible entropy production rate and dynamical activity rate.

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Outline

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Phys. Rev. E 113, 024129– Published 19 February, 2026
  • Received 22 May 2025
  • Accepted 27 January 2026
Article part of CHORUS
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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.

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