  Observations strongly suggest that filaments in galactic molecular clouds are
in a non-thermal state. As a simple model of a filament we study a
two-dimensional system of self-gravitating point particles by means of
numerical simulations of the dynamics, with various methods: direct $N$-body
integration of the equations of motion, particle-in-cell simulations and a
recently developed numerical scheme that includes multiparticle collisions in a
particle-in-cell approach. Studying the collapse of Gaussian overdensities we
find that after the damping of virial oscillations the system settles in a
non-thermal steady state whose radial density profile is similar to the
observed ones, thus suggesting a dynamical origin of the non-thermal states
observed in real filaments. Moreover, for sufficiently cold collapses the
density profiles are anticorrelated with the kinetic temperature, i.e., exhibit
temperature inversion, again a feature that has been found in some observations
of filaments. The same happens in the state reached after a strong perturbation
of an initially isothermal cylinder. Finally, we discuss our results in the
light of recent findings in other contexts (including non-astrophysical ones)
and argue that the same kind of non-thermal states may be observed in any
physical system with long-range interactions.
