  Thin liquid films are ubiquitous in natural phenomena and technological
applications. They have been extensively studied via deterministic hydrodynamic
equations, but thermal fluctuations often play a crucial role that needs to be
understood. An example of this is dewetting, which involves the rupture of a
thin liquid film and the formation of droplets. Such a process is thermally
activated and requires fluctuations to be taken into account self-consistently.
In this work we present an analytical and numerical study of a stochastic
thin-film equation derived from first principles. Following a brief review of
the derivation, we scrutinise the behaviour of the equation in the limit of
perfectly correlated noise along the wall-normal direction. The stochastic
thin-film equation is also simulated by adopting a numerical scheme based on a
spectral collocation method. The scheme allows us to explore the fluctuating
dynamics of the thin film and the behaviour of its free energy in the vicinity
of rupture. Finally, we also study the effect of the noise intensity on the
rupture time, which is in agreement with previous works.
