This chapter explains a simple fact that can seem surprising: systems far from equilibrium often evolve in ways that look like fluid motion sooner than one might expect. The authors review the idea of a hydrodynamic attractor. In plain terms, an attractor is a low-dimensional relation between a few observables that many different initial states converge to. A hydrodynamic attractor is one where that late-time relation matches the rules (constitutive relations) used in viscous fluid dynamics.

The chapter compares several theoretical approaches to show how attractors appear. The main testing ground is Bjorken flow, a highly symmetric model of longitudinal expansion used in studies of nuclear collisions. The authors discuss Müller–Israel–Stewart (MIS) type relaxation models and the BRSSS second-order theory (ways to write viscous fluid equations with relaxation), kinetic theory in the relaxation-time approximation (RTA), holography (a strong‑coupling calculational tool that maps some quantum systems to gravity problems), and classical Yang–Mills field simulations. Across these frameworks, different non-hydrodynamic excitations die away and many trajectories move toward a common relation between pressure anisotropy and a dimensionless measure of expansion.

The review also clarifies two different concepts that are often mixed up. Attractorization means that the system loses sensitivity to some directions in the space of initial states, so many different starts end up near the same curve. Hydrodynamization means the fluid constitutive relations become a good approximation to the true stress and currents. These can happen on different timescales. For example, rapid expansion can suppress initial differences before microscopic collisions have time to relax the system (called expansion-driven attraction). That suppression does not always imply the system has become a true fluid.