This fully-funded PhD studentship focuses on the hydrodynamic principles governing many-body systems out of equilibrium, exploring large-scale correlations, fluctuations, and quantum effects. The project involves both analytical and numerical methods, including the Bethe ansatz and Monte Carlo simulations. The successful candidate will work on a research project guided by Professor Benjamin Doyon under the EPSRC-funded UNIHYPE grant, aiming to uncover universal hydrodynamic principles and emergent physics in complex systems. A solid background in theoretical physics or applied mathematics and knowledge of numerical simulations are preferred.