  We analyze the probability distribution function (PDF) of work done on a
Luttinger liquid for an arbitrary finite duration interaction quench and show
that it can be described in terms a generalized Gibbs ensemble. We construct
the corresponding density matrix with explicit intermode correlations, and
determine the duration and interaction dependence of the probability of an
adiabatic transition and the PDF of non-adiabatic processes. In the
thermodynamic limit, the PDF of work exhibits a non-Gaussian maximum around the
excess heat, carrying almost all spectral weight. In contrast, in the small
system limit most spectral weight is carried by a delta peak at the energy of
the adiabatic process, and an oscillating PDF with dips at energies
commensurate to the quench duration and with an exponential envelope develops.
Relevance to cold atom experiments is also discussed.
