  The statistical measures of complexity defined by Lopez-Ruiz, Mancini, and
Calbet (LMC) and Shiner, Davison and Landsberg (SDL) are calculated as
functions of the number of particles for four quantum many-body systems, i.e.
atoms, nuclei, atomic clusters, and correlated atoms in a trap (bosons). A pair
of order and disorder strengths, evaluated for each system, can serve as a Pair
of Order-Disorder Indices (PODI), characterizing quantitatively order versus
disorder in any quantum system. According to the above classification, we
assign to bosons the complexity character of disorder, to atoms the character
of order, while nuclei and atomic clusters are (less) disordered and lie
between them. This criterion can be used to estimate the relative contribution
of order and disorder to complexity for other more complicated quantum systems
as well and even classical ones, if one is able to describe them
probabilistically. We also address the issue, whether those systems can grow in
complexity as the number of particles increases. Our comparative study
indicates that atoms are the only quantum system out of four, which is ordered,
with the ability to self-organize. We conjecture that this is an
information-theoretic reason that atoms are suitable as building blocks of
larger structures of biological interest i.e. molecules and macromolecules.
This is in the spirit of Wheeler's "it from bit" quote, the project to present
everything about the Universe in terms of information theory.
