Recently, stable meshfree methods for computational fluid mechanics have attracted rising interest. So far such methods mostly resort to similar strategies as already used for stabilized finite element formulations. In this study, we introduce an information theoretical interpretation of Petrov-Galerkin methods and Green's functions. As a consequence of such an interpretation, we establish a new class of methods, the so-called information flux methods. These schemes may not be considered as stabilized methods, but rather as methods which are stable by their very nature. Using the example of convection-diffusion problems, we demonstrate these methods' excellent stability and accuracy, both in one and higher dimensions.