The Boltzmann-Grad limit is a dilute-gas scaling in which particle size tends to zero while the collision rate stays of order one. In three dimensions, a grand canonical
activity 
accompanies interaction range 
. The packing fraction then tends to zero. For scaled
factorial marginal densities 
, convergence to
expresses independence of any fixed number of particles at the limiting kinetic scale.
Boltzmann-Grad Limit
See also
Boltzmann Equation, Probability MeasureExplore with Wolfram|Alpha
References
Bodineau, T.; Gallagher, I.; Saint-Raymond, L.; and Simonella, S. "Fluctuation Theory in the Boltzmann-Grad Limit." J. Stat. Phys. 180, 873-895, 2020. https://doi.org/10.1007/s10955-020-02549-5.Cite this as:
Weisstein, Eric W. "Boltzmann-Grad Limit." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Boltzmann-GradLimit.html