Where the things happen to be hidden about the Boltzmann equation nowadays?

For more than hundred years the Boltzmann equation has been accepted as the "ab initio" tool in physics, especially in Statistical Physics. Nevertheless, when at last this equation was checked out through the last like 10 years by Chinese physicist more scrupulously for validity, it has been found to be as the incorrect one.

This became the well known problem when a number of mostly online publications by C.Chen started to appear since 1990s - and we guess, the problem with Boltzmann equation still can not be solved within the Homogeneous One-Scale procedures used for derivation.

There are easily can be collected hundreds of papers and many books (there exist thousands and thousands of studies and texts - GOOGLE gives more than 700,000 links!) with the main goal as how to "explain" and explore this "ab initio" "theory" and equation. Well, how does it mean further that the theories were constructed (construed) at the beginning of 20th century for all over the physics and have been developed since then with this equation at the center, experiments have been run and money was spent and is being spent now ?

In previous, at least 6-8 decades the Boltzmann equation was regarded always not less as the "only" "ab initio" subject to use in research. Where are those researches and what consequences by that were brought in the respected fields? Gone? Forever?

Long ago I had a reservation regarding the Boltzmann equation and still, oh name, was hesitant to speak out loudly.

My reservations were sure apart of those recently discovered and stressed out by C.Chen. That unwillingness - it was basically concerning the averaging procedures in derivation of Boltzmann's equation, as of the volumetric phenomena not of a Point in space interactions collision term speculations and validation.

Because the point in space interaction collisions for point presented physical objects actually never happen! Unless, we accept silently that some volumes for a collision and some radius of particles play their fundamental role.

Now, after all these deliberations made by C.Chen I observe with relief that the total new way of doing statistical mechanics - via the real volume of particles and REAL VOLUME OF COLLISIONS AND INTERACTIONS, might be closer then few decades from now, the time needed for new generations of professors study the consequences and do not reject their own teachings.

We will touch down the few confined areas of Non-Local Two-Scale Boltzmann type Equation problems to put down the homogeneous medium mathematical ground, and then move to some extent into the formulation of Non-Local Upper Scale Two-Scale Boltzmann type Equation which is valid via procedures of Local-Nonlocal Scaled HSP-VAT Derivation main definitions.

We are addressing these and close issues in our sub-sections on Atomic scale media issues and in the sub-section -