  We study semi-classical communication in positivity-violating k-essence
scalar field theories, with superluminal modes propagating on a rolling
background. The self-interactions due to the non-linear nature of these
theories pose a constraint on the rate of superluminal information transfer. We
derive a novel bit rate bound on superluminal communication within a conceptual
model, to which a general class of k-essence theories naturally reduces. Our
result implies the possibility that, even if these positivity-violating
k-essence theories may not possess a maximal information propagation speed,
there is nevertheless an upper bound on the rate of information transfer.
