  We present some results obtained by applying the chaos theory on the
numerical study of one threedimensional, relativistic, many-body quark system.
The asymptotic freedom property is introduced by employing a harmonic term in
the bi-particle potential. In this context, we used also the outcome of a
semiclassical study, applied to the quark constituents of nucleons. Depending
on the initial temperature parameter, the system can evolve toward an
oscillating or an expansion regime. It is important to notice also a transition
region, characterized by a partial fragmentation (higher degree of order). This
effect can be observed near the critical temperature and is related to the
partial overcoming of the potential barrier (corresponding to the farthest
particles from the system). The degree of fragmentation is defined on the
Shannon entropy basis and using the graphs theory. For analyzing the expansion
tendency of one relativistic many-body system, we employed also the virial
coefficient.
