  The hydrodynamics of thin films is typically described using phenomenological
models whose connection to the microscopic particle dynamics is a subject of
ongoing research. Existing methods based on density functional theory provide a
good description of static thin films, but are not sufficient for understanding
nonequilibrium dynamics. In this work, we present a microscopic derivation of
the thin film equation using the Mori-Zwanzig projection operator formalism.
This method allows to directly obtain the correct gradient dynamics structure
along with microscopic expressions for the mobility and the free energy. Our
results are verified against molecular dynamics simulations for both simple
fluids and polymers.
