Phase Transition with Non-Thermodynamic States in Reversible
Polymerization
E. Ben-Naim and P.L. Krapivsky
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.
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