  It is discussed how the superstatistical formulation of effective Boltzmann
factors can be related to the concept of Kolmogorov complexity, generating an
infinite set of complexity measures (CMs) for quantifying information. At this
level, the information is treated according to its background, which means that
the CM depends on the inherent attributes of the information scenario. While
the basic Boltzmann factor directly produces the standard complexity measure
(SCM), it succeeds in the description of large-scale scenarios where the data
components are not interrelated with themselves, thus adopting the behaviour of
a gas. What happens in scenarios in which the presence of sources and sinks of
information cannot be neglected, needs of a CM other than the one produced by
the ordinary Boltzmann factor. We introduce a set of flexible CMs, without free
parameters, that converge asymptotically to the Kolmogorov complexity, but also
quantify the information in scenarios with a reasonable small density of
states. We prove that these CMs are obtained from a generalised relative
entropy and we suggest why such measures are the only compatible
generalisations of the SCM.
