Stochastic thermodynamic bounds on logical circuit operation

Abstract

Using a thermodynamically consistent, mesoscopic model for modern complementary metal-oxide-semiconductor transistors, we study an array of logical circuits and explore how their function is constrained by recent thermodynamic uncertainty relations when operating near thermal energies. For a single NOT gate, we find operating direction-dependent dynamics, and a trade-off between dissipated heat and operation time certainty. For a memory storage device, we find an exponential relationship between the memory retention time and energy required to sustain that memory state. For a clock, we find that the certainty in the cycle time is maximized at biasing voltages near thermal energy, as is the trade-off between this certainty and the heat dissipated per cycle. We identify a control mechanism that can increase the cycle time certainty without an offsetting increase in heat dissipation by working at a resonance condition for the clock. These results provide a framework for assessing thermodynamic costs of realistic computing devices, allowing for circuits to be designed and controlled for thermodynamically optimal operation.

8 pages, 4 figures

References in corpus (11)

• Thermodynamic uncertainty relation for biomolecular processes
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Probabilistic computing with p-bits
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Optimal Control in Stochastic Thermodynamics
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Limited-control optimal protocols arbitrarily far from equilibrium
• Large deviations theory for noisy non-linear electronics: CMOS inverter as a case study
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Adiabatic computing for optimal thermodynamic efficiency of information processing

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