  We investigate a reversible polymerization process in which individual
polymers aggregate and fragment at a rate proportional to their molecular
weight. We find a nonequilibrium phase transition despite the fact that the
dynamics are perfectly reversible. When the strength of the fragmentation
process exceeds a critical threshold, the system reaches a thermodynamic steady
state where the total number of polymers is proportional to the system size.
The polymer length distribution has a sharp exponential tail in this case. When
the strength of the fragmentation process falls below the critical threshold,
the steady state becomes non-thermodynamic as the total number of polymers
grows sub-linearly with the system size. Moreover, the length distribution has
an algebraic tail and the characteristic exponent varies continuously with the
fragmentation rate.
