Dynamic scaling in stochastic chemical kinetics

Universality classes are often comprised of seemingly dissimilar physical systems. Here, we draw a formal analogy between surface-roughening processes and the stochastic kinetics of fundamental chemical reactions. We simulate the chemical kinetics of several classes of reactions with Gillespie’s exact stochastic simulation algorithm and analyze the dynamic scaling of a quantity analogous to the surface roughness, w. For kinetics at chemical equilibrium considered thus far, the growth exponent is β=1/2. The dynamic exponent z, however, depends on the molecularity of the reaction. For simple cases these computational results can be verified analytically through the associated master equations. We observe a richer collection of exponents and scaling relations for nonequilibrium kinetics. Overall, these results suggest, just as in surface-roughening phenomena, that seemingly dissimilar chemical systems may also be partitioned into universality classes, some known and others new.