  We solve numerically a kinetic model of chiral polymerization in systems
closed to matter and energy flow, paying special emphasis to its ability to
amplify the small initial enantiomeric excesses due to the internal and
unavoidable statistical fluctuations. The reaction steps are assumed to be
reversible, implying a thermodynamic constraint among some of the rate
constants. Absolute asymmetric synthesis is achieved in this scheme. The system
can persist for long times in quasi- stationary chiral asymmetric states before
racemizing. Strong inhibition leads to long-period chiral oscillations in the
enantiomeric excesses of the longest homopolymer chains. We also calculate the
entropy production {\sigma} per unit volume and show that {\sigma} increases to
a peak value either before or in the vicinity of the chiral symmetry breaking
transition.
