Eur. Phys. J. B 73, 605-615 (2010)
https://doi.org/10.1140/epjb/e2010-00034-5

Differentiating information transfer and causal effect

¹ CSIRO Information and Communications Technology Centre, Locked Bag 17, North Ryde, 1670 NSW, Australia
² School of Information Technologies, The University of Sydney, 2006 NSW, Australia
³ Max Planck Institute for Mathematics in the Sciences, Inselstraße 22-26, 04103 Leipzig, Germany

Corresponding author: jlizier@it.usyd.edu.au

Received: 19 January 2009
Revised: 4 December 2009
Published online: 27 January 2010

Abstract

The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing measures, transfer entropy and information flow, which can be used separately to quantify information transfer and causal information flow respectively. We apply these measures to cellular automata on a local scale in space and time, in order to explicitly contrast them and emphasize the differences between information transfer and causality. We also describe the manner in which the measures are complementary, including the conditions under which they in fact converge. We show that causal information flow is a primary tool to describe the causal structure of a system, while information transfer can then be used to describe the emergent computation on that causal structure.