What is "h-theorem"

In classical statistical mechanics, the ''' H-theorem''', introduced by Ludwig Boltzmann in 1872, describes the tendency to increase in the quantity H (defined below) in a nearly- ideal gas of molecules. As this quantity H was meant to represent the entropy of thermodynamics, the H-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics.

The H-theorem is a natural consequence of the kinetic equation derived by Boltzmann that has come to be known as Boltzmann's equation. The H-theorem has led to considerable discussion about its actual implications, with major themes being:

• What is entropy? In what sense does Boltzmann's quantity H correspond to the thermodynamic entropy?
• Are the assumptions (especially the assumption of molecular chaos) behind Boltzmann's equation too strong? When are these assumptions violated?