  Virtually every organism gathers information about its noisy environment and
builds models from that data, mostly using neural networks. Here, we use
stochastic thermodynamics to analyse the learning of a classification rule by a
neural network. We show that the information acquired by the network is bounded
by the thermodynamic cost of learning and introduce a learning efficiency
$\eta\le1$. We discuss the conditions for optimal learning and analyse Hebbian
learning in the thermodynamic limit.
