Reversible and Irreversible Information Networks

It is shown that there exist information networks where messages can be sent (utilizing network coding) more easily in one direction than in the opposite direction. This is valid even though each channel is assumed to have the same capacity in both directions. It is shown that irreversible information networks only have solutions that use nonlinear network coding. This correspondence argues that this result is more surprising than it might appear at first sight and that it follows using ideas resembling the path integral in quantum mechanics.