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