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We analyze the probability distribution function (PDF) of work done on aLuttinger liquid for an arbitrary finite duration interaction quench and showthat it can be described in terms a generalized Gibbs ensemble. We constructthe corresponding density matrix with explicit intermode correlations, anddetermine the duration and interaction dependence of the probability of anadiabatic transition and the PDF of non-adiabatic processes. In thethermodynamic limit, the PDF of work exhibits a non-Gaussian maximum around theexcess heat, carrying almost all spectral weight. In contrast, in the smallsystem limit most spectral weight is carried by a delta peak at the energy ofthe adiabatic process, and an oscillating PDF with dips at energiescommensurate to the quench duration and with an exponential envelope develops.Relevance to cold atom experiments is also discussed.

Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid