# Learning Thermodynamics with Boltzmann Machines

arXiv: https://arxiv.org/abs/1606.02718 · HTML: https://mlsanity.com/paper/1606.02718/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2016.

## Built on by (most cited first, 16 of 16)

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- [Exploring the Energy Landscape of RBMs: Reciprocal Space Insights into Bosons, Hierarchical Learning and Symmetry Breaking](https://mlsanity.com/paper/2503.21536/) (2025)
- [Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines](https://mlsanity.com/paper/2511.19879/) (2025)
- [Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machines](https://mlsanity.com/paper/2602.09162/) (2026)
- [Thermodynamic properties of chemically disordered compounds via AI-driven estimation of partition function with the PULSE method](https://mlsanity.com/paper/2605.28594/) (2026)

## Abstract (arXiv)

A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance-sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.