Kinetic theory of dense gases has been a big challenge for a long time and some questions have not been answered yet. Problems like the role played by the entropy, the irreversibility criterion and the calculation of transport properties remain unsolved. Several approaches have tried to do such a task, however all of them have some uncomfortable piece, mainly in their foundations. In this sense the kinetic variational theory (KVT) has advanced some ideas which seem to be more solid than the heuristic proposals usually involved to work in this subject.  Here we want to call the attention on the maximum entropy formalism (MEF), which as a kind of kinetic variational theory starts with a functional representing the entropy, and by means of an extremum principle goes to the construction of a complete theory to study the behavior of dense gases. One of the main advantages of this approach comes when we realize that the entropy functional plays a central role, allowing for a consistent discussion of irreversibility.

As a first step, the formalism is developed at the kinetic level, it means that the description of the system will be done in terms of distribution functions. A closed set of kinetic equations and the entropy balance equation will show some interesting properties of the entropy production. Also an upper bound for entropy production is found in terms of the so called Fisher’s information integrals.

Moreover at a second level, we start with the entropy functional constructed in terms of distribution functions and its maximization allows us to obtain the hydrodynamical description. The consistency with the equations for the usual conserved variables is also shown and the relationship with other approaches will be explained.