# Nonlinear thermodynamic computing out of equilibrium

arXiv: https://arxiv.org/abs/2412.17183 · HTML: https://mlsanity.com/paper/2412.17183/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 22 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterial](https://mlsanity.com/paper/2311.00537/) (2023)
- [Thermodynamic Computing System for AI Applications](https://mlsanity.com/paper/2312.04836/) (2023)
- [Thermodynamic Computing](https://mlsanity.com/paper/1911.01968/) (2019)
- [Thermodynamic Neural Network](https://mlsanity.com/paper/1906.01678/) (2019)
- [Thermodynamic Computing via Autonomous Quantum Thermal Machines](https://mlsanity.com/paper/2308.15905/) (2023)
- [Is stochastic thermodynamics the key to understanding the energy costs of computation?](https://mlsanity.com/paper/2311.17166/) (2023)
- [Increasing the clock speed of a thermodynamic computer by adding noise](https://mlsanity.com/paper/2410.12211/) (2024)
- [Training neural networks using Metropolis Monte Carlo and an adaptive variant](https://mlsanity.com/paper/2205.07408/) (2022)
- [Adaptive AI-Driven Material Synthesis: Towards Autonomous 2D Materials Growth](https://mlsanity.com/paper/2410.10885/) (2024)

## Built on by (most cited first, 4 of 4)

- [Training thermodynamic computers by gradient descent](https://mlsanity.com/paper/2509.15324/) (2025)
- [Thermodynamic cost of inference and learning in physical neural networks](https://mlsanity.com/paper/2503.09980/) (2025)
- [CN101 - A Digital Thermodynamic Computer for Generative AI](https://mlsanity.com/paper/2608.00754/) (2026)
- [Online local learning for generative thermodynamic computing](https://mlsanity.com/paper/2609.15439/) (2026)

## Abstract (arXiv)

We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.