Broken detailed balance and non-equilibrium dynamics in noisy social learning models

We propose new Degroot-type social learning models with noisy feedback in continuous time. Unlike the standard Degroot framework, noisy information frameworks destroy consensus formation. On the other hand, noisy opinion dynamics converge to the equilibrium distribution that encapsulates correlations among agents’ opinions. Interestingly, such an equilibrium distribution is also a non-equilibrium steady state (NESS) with a non-zero probabilistic current loop. Thus, noisy information source leads to a NESS at long times that encodes persistent correlated opinion dynamics of learning agents. Our model provides a simple realization of NESS in the context of social learning. Other phenomena such as synchronization of opinions when agents are subject to a common noise are also studied.