  In this paper we prove the convergence to the stochastic Burgers equation
from one-dimensional interacting particle systems, whose dynamics allow the
degeneracy of the jump rates. To this aim, we provide a new proof of the second
order Boltzmann-Gibbs principle introduced in [Gon\c{c}alves, Jara 2014]. The
main technical difficulty is that our models exhibit configurations that do not
evolve under the dynamics - the blocked configurations - and are locally
non-ergodic. Our proof does not impose any knowledge on the spectral gap for
the microscopic models. Instead, it relies on the fact that, under the
equilibrium measure, the probability to find a blocked configuration in a
finite box is exponentially small in the size of the box. Then, a dynamical
mechanism allows to exchange particles even when the jump rate for the direct
exchange is zero.
