Field theory for classical systems. Entropic effects. Application to non homogeneous electrolytes

In contrast to other field theory approaches, we do not start from Gibbs partition function in terms of particles. The direct use of a field theory assumption leads to a simple formulation in terms of a Hamiltonian functional. The form of this functional party reminiscent of other field theory approaches and of the density functional theory. However, the formal similarity of the functional is misleading. In this paper, we intend to clarify some aspects which may lead to confusion when interpreting this field theory approach. We compare the role of quantum effects in the traditional approach and in field theory.