Information modification and particle collisions in distributed computation

Distributed computation can be described in terms of the fundamental operations of information storage, transfer, and modification. To describe the dynamics of information in computation, we need to quantify these operations on a local scale in space and time. In this paper we extend previous work regarding the local quantification of information storage and transfer, to explore how information modification can be quantified at each spatiotemporal point in a system. We introduce the separable information, a measure which locally identifies information modification events where separate inspection of the sources to a computation is misleading about its outcome. We apply this measure to cellular automata, where it is shown to be the first direct quantitative measure to provide evidence for the long-held conjecture that collisions between emergent particles therein are the dominant information modification events.