  Scattering processes often inevitably include the production of infrared
states, which are highly correlated with the hard scattering event, and
decohere the hard states. This can be described using the entropy of the hard
reduced density matrix, which is obtained from tracing over infrared states. We
determine this entropy for an asymptotically-free gauge theory by separating
the Hilbert space into hard and infrared states, and calculate it in a
leading-logarithmic approximation for jets. We find that the entropy increases
when the resolution scales defining the hard radiation are lowered, that this
entropy is related to the subjet multiplicity, and explore connections to using
jet images for machine learning, and the forward-scattering density matrix of
partons in a nucleon probed in deep-inelastic scattering.
