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

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