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The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic model ofnonequilibrium low-dimensional systems with spatiotemporal scale invariance,recently highlighting universal behavior in fluctuation statistics. Its spacederivative, namely the noisy Burgers equation, has played a very important rolein its study, predating the formulation of the KPZ equation proper, and beingfrequently held as an equivalent system. We show that, while differences in thescaling exponents for the two equations are indeed due to a mere spacederivative, the fluctuations behave in a remarkably different way: while KPZdisplays Tracy-Widom statistics, its derivative displays Gaussian behavior,hence being in a different universality class. We reach this conclusion viadirect numerical simulations of the equations, supported by a dynamicrenormalization group analysis of field statistics.

The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class