# Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium

## TL;DR

This paper introduces a novel method using structural complexity measures to analyze and distinguish spatio-temporal patterns in classical and quantum many-body systems out of equilibrium, even with limited data.

## Contribution

It develops a new approach to quantify complex spatio-temporal dynamics using minimal data, applicable to both classical and quantum systems, including non-equilibrium phases like discrete time crystals.

## Key findings

- Successfully distinguishes different dynamical regimes
- Provides a complete characterization of discrete time crystals
- Operates effectively with limited data and simple bitstring analysis

## Abstract

A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in many-body systems of completely different nature. In this work we provide a solution to this problem by adopting a structural complexity measure to quantify spatio-temporal patterns in the time-dependent digital representation of a system. On the basis of very limited amount of data our approach allows to distinguish different dynamical regimes and define critical parameters in both classical and quantum systems. By the example of the discrete time crystal realized in non-equilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings, which can be considered as a valuable alternative to previous studies based on the calculations of qubit correlation functions.