  It is well known that loss of information about a system, for some observer,
leads to an increase in entropy as perceived by this observer. We use this to
propose an alternative approach to decoherence in quantum field theory in which
the machinery of renormalisation can systematically be implemented: neglecting
observationally inaccessible correlators will give rise to an increase in
entropy of the system. As an example we calculate the entropy of a general
Gaussian state and, assuming the observer's ability to probe this information
experimentally, we also calculate the correction to the Gaussian entropy for
two specific non-Gaussian states.
