Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems
Abstract
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of hydrodynamics, the specific microscopic implementation should not matter. Here, we show that classical deterministic circuits provide a minimal, exact, and efficient platform that admits non-trivial hydrodynamic behaviour for deterministic but chaotic systems. By developing new techniques and focusing on 1D circuits as a proof of concept, we obtain the characteristic dynamics, including relaxation to Gibbs states, exact Euler equations, shocks, diffusion, and exact KPZ super-diffusion. Our methods can be easily generalised to higher dimensions or quantum circuits.
Cite
@article{arxiv.2503.08788,
title = {Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems},
author = {Sun Woo P. Kim and Friedrich Hübner and Juan P. Garrahan and Benjamin Doyon},
journal= {arXiv preprint arXiv:2503.08788},
year = {2025}
}