In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems. The method is articulated in various approximation protocols which allow to achieve increasing levels of accuracy, it is relatively simple to implement even for medium and large number of interactive particles, and uses tools and concepts from density functional theory. We test the method on the driven Hubbard dimer at half filling, and compare exact and approximate results. We show that the proposed method reproduces the average quantum work to high accuracy: for a very large region of parameter space (which cuts across all dynamical regimes) estimates are within 10% of the exact results.