So, we have asserted that there are two different sets of systems and structures - living and non-living. There is something very interesting about the differences between these two sets. Living things generate structures which are arbitrary, in the sense that the rules which govern the living structures are entirely psychological, except for the limitations placed upon living structures by the laws of the non-living nature.
Entirely psychological? Seems to be true. But since the laws of non-living nature govern everything, including the living things, let us make the obvious assumption that there is nothing that living things can do (including creating systems), which can go beyond what the non-living nature can do. This is meant to suggest that it is the non-living nature's laws and operations of symmetry and energy which govern living structures - that living structures which may seem arbitrary are, in fact, merely different sets of laws of nature.
All living structures necessarily exhibit attractive forces between its average constituents.
All living structures necessarily exhibit repulsive forces between some of its constituents.
All living structures necessarily exhibit an average equilibrium space between its constituents - personal space for human beings.
All living structures necessarily exhibit atomic properties such as segregation, solution, vacancies, interstitials, dislocations, etc.
Thus, even while the living and non-living sets of systems and structures are apparently mutually exclusive, they share some fundamental mathematical similarities - such as the symmetry principles, the tools for creating order in chaos.
More later.