  We examine the temporal evolution of the modular entropy and capacity (in
particular, the fluctuation of the entanglement entropy) for systems of
time-dependent oscillators coupled by a (time-dependent) parameter. Such
models, through the discretization procedure, fit into field theory problems
arising from quench phenomena or non-static spacetimes. First, we compare the
dynamics of the modular and Renyi entropies and derive the form of the modular
capacity for the single time-dependent oscillator as well as chains with
bipartite decompositions. In the latter case we analyse distinguished
periodicities during the evolution and the role of various boundary conditions.
Next, we focus on the dynamics of the capacity (fluctuation) of entanglement.
We compare the results obtained with the predictions of quasiparticles models;
in particular, we obtain a theoretical value of the initial slope of the
capacity for abrupt quenches. We study also continuous protocols with the
frequency that vanishes at plus (and minus) infinity, including a model in
which the frequency tends to the Dirac delta. All the above issues are
discussed with the emphasis on the analytical methods.
