  We conjecture a novel Generalized Second Law that can be applied in
cosmology, regardless of whether an event horizon is present: the generalized
entropy increases monotonically outside of certain hypersurfaces we call past
Q-screens. A past Q-screen is foliated by surfaces whose generalized entropy
(sum of area and entanglement entropy) is stationary along one future null
direction and increasing along the other. We prove that our Generalized Second
Law holds in spacetimes obeying the Quantum Focussing Conjecture. An analogous
law applies to future Q-screens, which appear inside evaporating black holes
and in collapsing regions.

High Energy Physics - Theory;General Relativity and Quantum Cosmology