Abstract
We provide a general theory of nonlinear electronic circuits subjected to thermal noise. The devices constituting the circuit can have arbitrary 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.
- Received 1 October 2020
- Revised 2 July 2021
- Accepted 8 July 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031064
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)
Popular Summary
Thermal fluctuations in complex electronic circuits are one of the limiting factors preventing the design of faster computers with lower energy demands. Also, new computing schemes are being considered where thermal fluctuations are exploited as a resource to solve problems that require randomness, thus enabling considerable energy savings. However, thermal fluctuations are usually described with ad hoc treatments involving approximations that are difficult to control. In this article, we show how to construct rigorous stochastic models of complex electronic circuits at the single electron level and in a thermodynamically consistent way.
To do this, we leverage recent developments in the field of stochastic thermodynamics that provide new rigorous tools and concepts of universal validity to understand the role of thermal fluctuations in many different systems. When we combine these developments with modeling methods used in engineering, the resulting formalism allows us to build stochastic models of a large family of electronic circuits with practical relevance. In particular, we apply it to the kind of circuits used nowadays to design computers.
As a first nontrivial application, we propose and study a design of a stochastic neuron (a basic component for the physical implementation of artificial neural networks) that uses thermal fluctuations as a resource and that can be built with the same technology that powers regular computers. Thus, our work provides bridges between statistical physics, thermodynamics, and computer design.
