  Establishing a description for confinement is not something simple. In order
to try to understand a little about this phenomenon, we will explore the
thermodynamics of models that try to describe it in terms of propagators with
violation of positivity. In this work, "confinement" is always understood in
the sense of positivity violation of the propagator of the elementary fields.
For simplicity, we will define a model for scalar fields with a momentum
dependent and nonlocal mass term. One of our objectives is to verify the
thermodynamic properties of this Lagrangian in order to analyze possible
inconsistencies. For this we use the functional formalism of Quantum Field
Theory at finite temperature, from which we obtain the partition function and,
consequently, the thermodynamic variables such as pressure, energy density,
entropy density, etc. Then, we obtain the two-point function at finite
temperature of the scalar field, in order to study whether or not there is a
restoration of positivity (hence, deconfinement, in our language).
