Fig. 1: Emergence of hydrodynamic fluctuations in a chaotic quantum system.
From: Emergence of fluctuating hydrodynamics in chaotic quantum systems
a, In an out-of-equilibrium quantum system without large-scale density variations, local expectation values (such as density) rapidly relax, while entanglement keeps spreading across the system on much longer timescales. b, Thus, a subsystem becomes increasingly entangled with its environment, leading to fluctuations of observables in the subsystem that equilibrate on a much slower timescale than local expectation values. Eventually, thermal equilibrium is reached, as described by the eigenstate thermalization hypothesis (ETH). c, This slow hydrodynamic equilibration of fluctuations is conjectured to be classically described by FHD, which predicts the time evolution of the statistics of a coarse-grained density n(x, t) driven by statistical noise.
