The electron star is a holographic bulk setup which consists of a non-extremal AdS-Reissner-Nordstr"{o}m black brane and an ideal gas of electrons. The gravitational system is dual to a field theory with interacting fractionalised and mesonic degrees of freedom, and is thermodynamically favoured over a pure black brane scenario. The electron gas in this Einstein-Maxwell-fluid theory is treated as being at zero temperature. The system is thus gravitationally stable but is {it not} in thermodynamic equilibrium. After analysing thermodynamic properties of the background, we compute the quasi-normal mode spectrum and correlation functions of gauge-invariant quantities on the boundary to study momentum and charge transport in the shear sector. We perform a detailed analysis of the hydrodynamic diffusion mode dispersion relation and compare our numerical results with thermodynamic predictions. We show that they only agree at very low temperature and near transition to a purely black brane background. We thus conclude that in accordance with expectations, hydrodynamics and thermodynamics cannot successfully describe a system out of thermal equilibrium. This provides further evidence for the importance of holographic studies of thermalisation, hydrolysation and out-of-equilibrium phenomena.