Final answer:
The classical limits define when classical physics can be applied, and under these limits, quantum distribution laws diminish to the classical Maxwell-Boltzmann distribution which is a predictable distribution of molecular speeds in a gas.
Step-by-step explanation:
The classical limits pertain to conditions under which classical physics is applicable. Classical physics applies when the matter in question is moving at velocities much less than the speed of light (typically less than 1%), is large enough to be seen with a microscope, and when only weak gravitational fields are present. The transition of quantum distribution laws to the classical Maxwell-Boltzmann distribution occurs under these classical limits. The Maxwell-Boltzmann distribution describes a predictable distribution of molecular speeds in a gas, based on the kinetic theory. As quantum numbers increase, quantum probability distributions show a diminishing quantum character and increasingly resemble classical distributions. This is in line with Bohr's correspondence principle, where quantum mechanics is seen to converge to classical physics at large quantum numbers or under classical limits.