Planetary Complexity Revealed by the Joint Differential Entropy of Eigencolours

We propose a measure, the joint differential entropy of eigencolours, for determining the spatial complexity of exoplanets using only spatially unresolved light curve data. The measure can be used to search for habitable planets, based on the premise of a potential association between life and exoplanet complexity. We present an analysis using disk-integrated light curves from Earth, developed in previous studies, as a proxy for exoplanet data. We show that this quantity is distinct from previous measures of exoplanet complexity due to its sensitivity to spatial information that is masked by features with large mutual information between wavelengths, such as cloud cover. The measure has a natural upper limit and appears to avoid a strong bias toward specific planetary features. This makes it a candidate for being used as a generalisable measure of exoplanet habitability, since it is agnostic regarding the form that life could take.