In this paper we present an analysis of information transfer based on Landauer's principle (i.e. erasure of information is associated with an increase in entropy), as well as considerations of analyticity and causality. We demonstrate that holomorphic functions allowing complete analytic continuation cannot propagate any information, such that information transfer only occurs with analytic functions having points of non-analyticity (i.e. meromorphic functions). Such points of non-analyticity (or discontinuities) are incompatible with adiabaticity, so that information transfer must always be accompanied by a change in entropy: a dynamic reformulation of Landauer's Principle. In addition, since Brillouin proved that discontinuities cannot travel faster than the speed of light c, this also implies that information cannot be transferred at superluminal speeds.

5 pages, to be published in Optics Communications