Abstract:
Since the emergence of systematic science it has been recognized that a natural phenomenon can be described
by different models that vary in their complexity and their ability to capture the details of the features
relevant at the required level of the resolution. It has been tacitly assumed that whenever two such models
are applicable at the same level, they must provide equivalent descriptions of the phenomenon. One of the
earliest and most celebrated examples of this type is offered by gas
flow which can be described either by
the Boltzmann equation at a suitably understood molecular level or by the Euler or Navier-Stokes equations
at the level of continuum. More precisely, the
flow of a gas as a continuous medium, or, in other words,
at the macro level, can be explained in more detail by analysing elementary collisions between pairs of
molecules. Thus, the Boltzmann equation is often recognized as a more detailed equation of gas at the
so-called mesoscopic, or kinetic, level from which macroscopic properties of gas, such as density, momentum
or temperature, can be derived. It should be noted that one can model gas at an even more fundamental,
or micro, level by tracing the motion of individual molecules by solving the system of the Newton equations
that describe their interactions.
