In a recent work with P. Goncalves, we introduced what we called the second-order Boltzmann-Gibbs principle, and we used it in order to show that KPZ equation appears as the scaling limit of density fluctuations of weakly asymmetric, conservative systems in dimension 1. In this talk we will present other applications of of this principle, ranging from functional limit theorems for additive functionals of particle systems to the derivation of a novel equation, which we call fractional KPZ equation. This equation has the same scaling exponents of the KPZ universality class, but it is qualitatively different from the conjectured scaling limit of the KPZ universality class. This fact makes this equation a candidate for the scaling limit of a still unknown universality class, which we conjecture to have some relation with heat anomalous conduction in dimension d=1. Joint work with P. Goncalves.