  In the particular case of a concave flux function, we are interested in the
long time behaviour of the nonlinear process associated to the one-dimensional
viscous scalar conservation law. We also consider the particle system obtained
by remplacing the cumulative distribution function in the drift coefficient of
this nonlinear process by the empirical cdf. We first obtain trajectorial
propagation of chaos result. Then, Poincar\'e inequalities are used to get
explicit estimates concerning the long time behaviour of both the nonlinear
process and the particle system.
