Certainly non psychological, there are many nature like entropic, illusional (block universe theory), Aristotelian (that which realize change), mathematical (Smolin, Bergson).
Still none of these characterizes properly Galilean physics or the bulk of established literature of physics.
What do you think is the nature of time that characterizes best the meaning it is ascribed in its use and in the framework of the definitional choices of physical parameters in theories modern physics?