  Physical kinetic roughening processes are well known to exhibit universal
scaling of observables that fluctuate in space and time. Are there analogous
dynamic scaling laws that are unique to the chemical reaction mechanisms
available synthetically and occurring naturally? Here, we formulate two
complementary approaches to the dynamic scaling of stochastic fluctuations in
thermodynamic observables at and away from equilibrium. Both analytical
expressions and numerical simulations confirm our dynamic scaling ans{\"a}tze
with their associated exponents, functions, and laws. A survey of common
chemical mechanisms reveals classes that organize according to the molecularity
of the reactions involved, the nature of the reaction vessel and external
reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the
reaction network. Coupled reactions capable of chemical feedback can
transition, sometimes sharply, between these classes with the variation of
experimental parameters such as temperature. While path observables like the
dynamical activity have scaling exponents that are time-independent,
fluctuations in the entropy production and flow can have time-dependent scaling
exponents and self-averaging properties as a result of temporal correlations
that emerge during thermodynamically irreversible processes. Altogether, these
results establish dynamic universality in the nonequilibrium fluctuations of
thermodynamic observables for well-mixed chemical reactions.
