Family-Vicsek universality of the binary intrinsic dimension of nonequilibrium data

TL;DR

This paper demonstrates that the binary intrinsic dimension (BID) of nonequilibrium growth data exhibits Family-Vicsek scaling, revealing universal properties and correlations in out-of-equilibrium systems, thus providing a new tool for their analysis.

Contribution

It introduces the application of binary intrinsic dimension to nonequilibrium data and shows it captures universal scaling behavior similar to surface roughness.

Findings

BID exhibits Family-Vicsek dynamical scaling in nonequilibrium data.

BID retains essential physical information after binary reduction.

The approach offers a new way to characterize out-of-equilibrium dynamics.

Abstract

The intrinsic dimension (ID) is a powerful tool to detect and quantify correlations from data. Recently, it has been successfully applied to study statistical and many-body systems in equilibrium, yet its application to systems away from equilibrium remains largely unexplored. Here we study the ID of nonequilibrium growth dynamics data, and show that even after reducing these data to binary form, their binary intrinsic dimension (BID) retains essential physical information. Specifically, we find that, akin to the surface width, it exhibits Family-Vicsek dynamical scaling -- a fundamental feature to describe universality in surface roughness phenomena. These findings highlight the ability of the BID to correctly discern key properties and correlations in nonequilibrium data, and open an avenue for alternative characterizations of out-of-equilibrium dynamics.