Entrainment is a known adaptation mechanism that causes interaction participants to adapt or synchronize their acoustic characteristics. Understanding how interlocutors tend to adapt to each other's speaking style through entrainment involves measuring a range of acoustic features and comparing those via multiple signal comparison methods. In this work, we present a turn-level distance measure obtained in an unsupervised manner using a Deep Neural Network (DNN) model, which we call Neural Entrainment Distance (NED). This metric establishes a framework that learns an embedding from the population-wide entrainment in an unlabeled training corpus. We use the framework for a set of acoustic features and validate the measure experimentally by showing its efficacy in distinguishing real conversations from fake ones created by randomly shuffling speaker turns. Moreover, we show real world evidence of the validity of the proposed measure. We find that high value of NED is associated with high ratings of emotional bond in suicide assessment interviews, which is consistent with prior studies.