Fire is one of only two names shared between the Wu Xing and the Greek four elements, and the overlap invites a comparison that the systems do not support. The Greek fire is a material out of which things are composed. The Chinese huo is a phase in a cycle, defined by what it produces and what it restrains rather than by what it is made of.
In the generating cycle, sheng, Wood produces Fire and Fire produces Earth, the second step read as the ash left by burning. In the overcoming cycle, ke, Water restrains Fire and Fire restrains Metal, since fire melts what metal is worked from. Fire is therefore the child of Wood, the parent of Earth, the master of Metal and the subject of Water, all at once, and no one of those relations can be dropped without the phase losing its meaning.
In the classical Chinese medical literature Fire is the phase of the heart and the small intestine, of the tongue, of the blood vessels, of summer, of the south, of the colour red, of the bitter flavour and of joy among the emotions. It is also the phase most often given a doubled treatment in the medical texts, where a second, ministerial fire is distinguished from the sovereign fire of the heart, an elaboration the other four phases do not receive.
These are correspondences within a named system. They are recorded here as description, not as instruction, and not as claims in the atlas's own voice.
Sources Science and Civilisation in China, Volume 2: History of Scientific ThoughtJoseph Needham with Huangdi Neijing (The Yellow Emperor's Inner Classic)Traditionally attributed to Huangdi; actual authorship unknown