# Theory of hierarchy

In statistical physics we consider a system of a huge number of particles. Each particle on its own is characterized by parameters (like mass or charge) and dynamical quantities (like momentum, energy). Interactions between particles are supposed to be known.

If one follows the path of a particular particle then one sees that it's dynamical quantities change rapidly with time (in collisions or by external fields) and two neighboring particles may have quite different values of energy or momentum at the same time.

However, when closed system of large number of such particles is observed some properties of particles become "insignificant" (like charge, which is mostly compensated in massive bodies) while others turn out to become constants (like energy of some volume of a body, the variation of which decreases as $1/\sqrt{N}$).
Most interestingly, some new properties emerge (like volume or pressure) that cannot be "well-defined" for a system of "not-so-many" particles.

We can see this kind of transformations of properties in many other situations. E.g. in astrophysics - hot gases collapse to form stars and we can find physical laws specific to stars, stars in turn form clusters that follow their own dynamics. In biology cells form organs.

My question - is there any mathematical theory of such transformations? A theory to predict which properties will become insignificant, what new properties will arise?