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.8 MoreReceived 1 October 2020Revised 2 July 2021Accepted 8 July 2021DOI:https://doi.org/10.1103/PhysRevX.11.031064Published 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 SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium & irreversible thermodynamicsThermodynamicsThermodynamics of computationPhysical SystemsStochastic dynamical systemsStochastic networksStatistical PhysicsNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsNetworks