Pattern recognition minimizes entropy production in a neural network of electrical oscillators

We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Hölzel and Krischer, 2011 13]). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈dS/dt〉$〈\mathrm{d}S/\mathrm{d}t〉$ of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈dS/dt〉$〈\mathrm{d}S/\mathrm{d}t〉$ is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.