Contextuality scenarios arising from networks of stochastic processes

TL;DR

This paper introduces a classical source of contextual empirical models based on networks of stochastic processes, showing that their long-term behavior naturally leads to contextuality similar to quantum phenomena.

Contribution

It presents a novel classical framework for contextual empirical models derived from stochastic process networks, expanding understanding beyond quantum origins.

Findings

Networks of stochastic processes produce inherently contextual empirical models.

Long-term behavior of these networks often results in strong contextuality.

Classical stochastic networks can mimic quantum-like contextual phenomena.

Abstract

An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations are coherent, in the sense that the distribution on a face of a simplex coincides with the marginal of the distribution over the entire simplex. An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. Contextual empirical models arise naturally in quantum theory, giving rise to some of its counter-intuitive statistical consequences. In this paper we present a different and classical source of contextual empirical models: the interaction among many stochastic processes. We attach an empirical model to the ensuing network in which each node represents an open stochastic process with input and output random variables. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.