Landauer's principle and information at the cosmological horizon

Abstract: We show that the information loss at the cosmological apparent horizon in an expanding universe does not obey Landauer's principle for efficient information erasure. This is in contrast to what happens for black holes, where the principle is upheld exactly. We discuss about the implications this result provides for the differences between information loss at black holes and that at the cosmological apparent horizon, which we term the "Cosmological Information Paradox". We also discuss how this result may point towards incompleteness of quasi-local descriptions of energy and could also point towards different thermodynamic settings in gravitational systems and how information thermodynamics as we know it may have limits to its applicability.