  In this work, we analyze the nonequilibrium thermodynamics of a class of
neural networks known as Restricted Boltzmann Machines (RBMs) in the context of
unsupervised learning. We show how the network is described as a discrete
Markov process and how the detailed balance condition and the Maxwell-Boltzmann
equilibrium distribution are sufficient conditions for a complete
thermodynamics description, including nonequilibrium fluctuation theorems.
Numerical simulations in a fully trained RBM are performed and the heat
exchange fluctuation theorem is verified with excellent agreement to the
theory. We observe how the contrastive divergence functional, mostly used in
unsupervised learning of RBMs, is closely related to nonequilibrium
thermodynamic quantities. We also use the framework to interpret the estimation
of the partition function of RBMs with the Annealed Importance Sampling method
from a thermodynamics standpoint. Finally, we argue that unsupervised learning
of RBMs is equivalent to a work protocol in a system driven by the laws of
thermodynamics in the absence of labeled data.
