  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.
