Maximum entropy principle revisited

We study the effect of the Maximum Entropy Principle (MEP) on the thermodynamic behaviour of gases. The MEP relies on the kinetic theory of gases and yields the local constitutive equations of Extended Thermodynamics. There are two extreme cases on the scale of the kinetic theory: Dominance of particle interactions and free flight. In its current form the MEP gives the phase density that maximizes the entropy at each instant of time. This is appropriate in case of dominant particle interaction but it is not adequate for free flight. Here we introduce a modified MEP that is capable to link both extreme cases. To illustrate the way the modified MEP works, we consider an example which leads in the case of dominant particle interactions to the Euler equations. In addition there results a representation theorem that contains the global solutions of the Euler equations with all shock interactions for arbitrary large variations of the initial data.