  After Boltzmann and Gibbs, the notion of disorder in statistical physics
relates to ensembles, not to individual states. This disorder is measured by
the logarithm of ensemble volume, the entropy. But recent results about measure
concentration effects in analysis and geometry allow us to return from the
ensemble--based point of view to a state--based one, at least, partially. In
this paper, the order--disorder problem is represented as a problem of relation
between distance and measure. The effect of strong order--disorder separation
for multiparticle systems is described: the phase space could be divided into
two subsets, one of them (set of disordered states) has almost zero diameter,
the second one has almost zero measure. The symmetry with respect to
permutations of particles is responsible for this type of concentration.
Dynamics of systems with strong order--disorder separation has high average
acceleration squared, which can be interpreted as evolution through a series of
collisions (acceleration--dominated dynamics). The time arrow direction from
order to disorder follows from the strong order--disorder separation. But,
inverse, for systems in space of symmetric configurations with ``sticky
boundaries" the way back from disorder to order is typical (Natural selection).
Recommendations for mining of molecular dynamics results are presented also.
