Decomposing non-Markovian History Dependence

Non-Markovian stochastic processes, where the next state of a system depends not only on the current state, but also on states far into the past, are ubiquitous in biology, from epigenetic memory, to neural activity, to learning and adaptation in the behavior of all living organisms. Nevertheless, we lack a general framework for quantifying historical dependencies in such processes. To address this, we propose an information-theoretic approach to decompose history-dependence in systems with non-Markovian dynamics, quantifying the information encoded in dependencies of each order. In a family of simple models for non-Markovian dynamics, we show that this framework correctly identifies history-dependence in (finite-order) Markovian and non-Markovian dynamics, even when autocorrelations fail to reflect true history-dependence. We apply our framework to study history dependence in animal behavior data, and explore how non-Markovianity emerges from coarse-graining. Our results reveal both convergent information scaling and a unique timescale that maximizes non-Markovian information.