  We show that the information loss at the cosmological apparent horizon in an
expanding universe has a direct correspondence with the Landauer principle of
information dynamics. We show that the Landauer limit is satisfied in this
case, which implies that the information erasure at the cosmological apparent
horizon happens in the most efficient way possible. We also show that our
results hold for extensions of the standard entropy formulations. We also
discuss about the connections this result provides between information loss at
black holes and that at the cosmological apparent horizon, and we term the
"Cosmological Information Paradox". This is the first work which directly
provides a correspondence between information dynamics and expanding cosmic
horizons, and we discuss several interesting implications of this result.
