Many models of systems with discrete state space can be set in terms of interacting exclusion processes with a Markovian dynamics (deformations of curves, reactions with regard to polymers or biology, etc). Then the interplay between discrete and continuous description is ubiquitous, and, as usual in statistical physics, often requires the derivation of hydrodynamic limits after convenient scalings. In this respect, starting from examples, a seemingly new approach is presented, which relies on variational calculus and functional integration.