  Hebbian learning theory is rooted in Pavlov's Classical Conditioning. In
addition, while mathematical models of the former have been proposed and
studied in the past decades, especially in spin glass theory, only recently it
has been numerically shown that the Pavlovian neural and synaptic dynamics
mechanisms give rise to synaptic weights that correspond to the Hebbian
learning rule. In this paper, we show that we can analytically prove this
result. Moreover, we obtain the Pavlovian dynamics directly with statistical
mechanics considerations, so that we can model the whole process within the
same framework. Then, we test and study the model in different numerical
settings. Finally, drawing from evidence on pure memory reinforcement during
sleep stages, we show how the proposed model can simulate neural networks that
undergo sleep-associated memory consolidation processes, thereby proving the
compatibility of Pavlovian learning.
