  A possible solution of the information paradox can be sought in quantum
information scrambling. In this paradigm, it is postulated that all information
entering a black hole is rapidly and chaotically distributed across the event
horizon making it impossible to reconstruct the information by means of any
local measurement. However, in this scenario the effects of decoherence are
typically ignored, which may render information scrambling moot in cosmological
settings. In this work, we develop key steps towards a thermodynamic
description of information scrambling in open quantum systems. In particular,
we separate the entropy production into contributions arising from scrambling
and decoherence, for which we derive statements of the second law. This is
complemented with a numerical study of the Sachdev-Ye-Kitaev, Maldacena-Qi,
XXX, mixed field Ising, Lipkin-Meshkov-Glick models in the presence of
decoherence in energy or computational basis.
