# Incoherence: A Generalized Measure of Complexity to Quantify Ensemble Divergence in Multi-Trial Experiments and Simulations

## TL;DR

This paper introduces a new measure called 'incoherence' to quantify complexity and uncertainty in multi-trial experiments and simulations.

## Contribution

The novelty lies in using an adapted Jensen-Shannon Divergence to define incoherence as a generalized complexity measure.

## Key findings

- Incoherence was compared to established statistical tests on both continuous and discrete data.
- The measure effectively identifies key complex system traits like sensitivity to initial conditions and criticality.
- It also captures how systems respond to perturbations.

## Abstract

Complex systems pose significant challenges to traditional scientific and statistical methods due to their inherent unpredictability and resistance to simplification. Accurately detecting complex behavior and the uncertainty which comes with it is therefore essential. Using the context of previous studies, we introduce a new information-theoretic measure, termed “incoherence”. By using an adapted Jensen-Shannon Divergence across an ensemble of outcomes, we quantify the aleatoric uncertainty of the system. First we compared this measure to established statistical tests using both continuous and discrete data. Before demonstrating how incoherence can be applied to identify key characteristics of complex systems, including sensitivity to initial conditions, criticality, and response to perturbations.