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