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

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 $k_{\mathrm{B}}T$ 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.

17 pages, 11 figures, 2 tables (+Supplemental Material: 6 pages, 5 figures, 1 table)

References in corpus (21)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
• On-chip Maxwell's demon as an information-powered refrigerator
• Universal trade-off relation between power and efficiency for heat engines
• Thermodynamics with continuous information flow
• First and Second Law of Thermodynamics at strong coupling
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Stochastic thermodynamics of resetting
• Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics
• Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse-graining
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Thermodynamics of Gambling Demons
• Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Thermodynamics of stochastic Turing machines
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Counting Statistics of Single Electron Transport in Bilayer Graphene Quantum Dots
• Autonomous demon exploiting heat and information at the trajectory level
• Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting
• Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes