2012/10/18 by Peter Gmeiner, Gmeiner, Peter
Computer Science · Engineering · Neuroscience · #94A17 #Advanced Memory and Neural Computing #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Mathematical Physics (math-ph) #Neural dynamics and brain function
paper · pdf · doi:10.48550/arxiv.1210.5058
openalex publication_date 2012/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The persistent mutual information (PMI) is a complexity measure for stochastic processes. It is related to well-known complexity measures like excess entropy or statistical complexity. Essentially it is a variation of the excess entropy so that it can be interpreted as a specific measure of system internal memory. The PMI was first introduced in 2010 by Ball, Diakonova and MacKay as a measure for (strong) emergence. In this paper we define the PMI mathematically and investigate the relation to excess entropy and statistical complexity. In particular we prove that the excess entropy is an upper bound of the PMI. Furthermore we show some properties of the PMI and calculate it explicitly for some example processes. We also discuss to what extend it is a measure for emergence and compare it with alternative approaches used to formalize emergence.