Quantum-inspired tools in classical many-body dynamics

The exponentially large Hilbert space of quantum many-body systems provides a natural playground to explore how correlations spread dynamically. As a prominent example, the case of unitary dynamics following a quantum quench has been extensively studied in terms of entanglement entropy, that can describe correlations in a comprehensive (nonlocal) way. By contrast, in the case of classical dynamics the attention has remained limited mostly to order parameters and few-body correlation functions. However, the phase space of a classical many-body system can also be exponentially large, which begs the question about the dynamics of correlations beyond few-body observables in a classical setting. Here, we show that many of the salient features of the entanglement dynamics following a quantum quench (e.g., linear growth to an extensive value) also emerge in classical Hamiltonian dynamics, both for the mutual information and for a suitably defined classical analogue of the entanglement entropy. To demonstrate the generality of our approach, we then apply it in the setting of cellular automata. Looking ahead, our study opens new possibilities across physics, information theory, and statistics.