Stochastic Thermodynamics of Nonlinear Electronic Circuits: A Realistic Framework for Computing Around kT

We provide a general theory of nonlinear electronic circuits subjected to thermal noise. The devices constituting the circuit can have arbitrary I-V curves but must display shot noise. This theory includes tunnel junctions, diodes, and MOS transistors in subthreshold operation, among others. The stochastic nonequilibrium thermodynamics of these circuits is also established. The irreversible entropy production is expressed in terms of thermodynamic potentials and forces, and its fluctuations satisfy fluctuation theorems. Our theory is ideally suited to formulate a thermodynamics of computing with realistic architectures, where the reduction in transistor size and operating voltages make thermal fluctuations increasingly important. We demonstrate this point in two ways: first, by proposing a stochastic model of a CMOS inverter whose actual transfer function deviates from the deterministic one due to nonequilibrium fluctuations, and, second, by proposing a low-power full-CMOS design for a probabilistic bit (or binary stochastic neuron) exploiting intrinsic noise.

Automated summary

A general theory of nonlinear electronic circuits subjected to thermal noise is provided, involving devices like tunnel junctions, diodes, and MOS transistors in subthreshold operation. The stochastic nonequilibrium thermodynamics of these circuits is established, with irreversible entropy production expressed in terms of thermodynamic potentials and forces, and its fluctuations satisfying fluctuation theorems. The theory is shown to be applicable in formulating a thermodynamics of computing with realistic architectures, where thermal fluctuations play an increasingly important role due to reduction in transistor size and operating voltages.