Entropy Evolution in Consensus Networks

We investigate the evolution of the network entropy for consensus dynamics in classical and quantum networks. We show that in the classical case, the network differential entropy is monotonically non-increasing if the node initial values are continuous random variables. While for quantum consensus dynamics, the network's von Neumann entropy is in contrast non-decreasing. In light of this inconsistency, we compare several distributed algorithms with random or deterministic coefficients for classical or quantum networks, and show that quantum algorithms with deterministic coefficients are physically related to classical algorithms with random coefficients.