  Conserved-charge densities are very special observables in quantum many-body
systems as, by construction, they encode information about the dynamics.
Therefore, their evolution is expected to be of much simpler interpretation
than that of generic observables and to return universal information on the
state of the system at any given time. Here we study the dynamics of the
fluctuations of conserved U(1) charges in systems that are prepared in
charge-asymmetric initial states. We characterise the charge fluctuations in a
given subsystem using the full-counting statistics of the truncated charge and
the quantum entanglement between the subsystem and the rest resolved to the
symmetry sectors of the charge. We show that, even though the initial states
considered are homogeneous in space, the charge fluctuations generate an
effective inhomogeneity due to the charge-asymmetric nature of the initial
states. We use this observation to map the problem into that of charge
fluctuations on inhomogeneous, charge-symmetric states and treat it using a
recently developed space-time duality approach. Specialising the treatment to
interacting integrable systems we combine the space-time duality approach with
generalised hydrodynamics to find explicit predictions.
