  When searching for inhabited exoplanets, understanding the boundaries of the
habitable zone around the parent star is key. If life can strongly influence
its global environment, then we would expect the boundaries of the habitable
zone to be influenced by the presence of life. Here using a simple abstract
model of `tangled-ecology' where life can influence a global parameter,
labelled as temperature, we investigate the boundaries of the habitable zone of
our model system. As with other models of life-climate interactions, the
species act to regulate the temperature. However, the system can also
experience `punctuations', where the system's state jumps between different
equilibria. Despite this, an ensemble of systems still tends to sustain or even
improve conditions for life on average, a feature we call Entropic Gaia. The
mechanism behind this is sequential selection with memory which is discussed in
detail. With this modelling framework we investigate questions about how Gaia
can affect and ultimately extend the habitable zone to what we call the Gaian
habitable zone. This generates concrete predictions for the size of the
habitable zone around stars, suggests directions for future work on the
simulation of exoplanets and provides insight into the Gaian bottleneck
hypothesis and the habitability/inhabitance paradox.
