Enhancing associative memory recall in non-equilibrium materials through activity.

Memory is a key feature in many biological and physical systems. The Hopfield model is a paradigm for explaining associative memory. Under equilibrium conditions, the Hopfield network can store and retrieve upto 0.14N patterns, where N is the number of spins in the system. Recent works have explored how the capacity of the Hopfield model can be increased through various schemes which include changing the form of learning and changing the form of interactions between the different degrees of freedom. Since biological systems work far from equilibrium, we want to address this through the effect of nonequilibrium activity in the system. We introduce activity into the system as AOUP noise which breaks detailed balance and takes the system out of equilibrium. Under such conditions the system can store and retrieve more patterns than the equilibrium case at the same "Effective" temperature. Using a perturbative scheme we probe the change in the free energy landscape of this active system and show the rate of entropy production helps the system to access memory regions which were previously inaccessible. Using the Martin-Siggia-Rose Lagrangian formalism we also derive a set of exact equations which predict conditions of improved memory.