This equation shares the same dynamics as a circle of equally spaced balls colored black or white, which move in a clockwise direction at the same speed and change color whenever they pass a mark on the circle; that construction is the Kac ring model.
This equation shares the same dynamics as a circle of equally spaced balls colored black or white, which move in a clockwise direction at the same speed and change color whenever they pass a mark on the circle; that construction is the Kac ring model. Applying time-reversal invariance to this equation can be used to show that it is only strictly valid when the integral over velocity space of f times the natural log of f is at a local maximum. The derivation of thisequation assumes that the velocities and positions of molecules are statistically independent, a condition called "molecular chaos." For a gas of particles which only interact via binary collisions, this equation gives an expression for the time evolution of the non-equilibrium distribution function. The H-theorem is derived using, for 10 points, what "transport equation" of statistical mechanics, named for a scientist who proposed a logarithmic formula for entropy? 
This equation shares the same dynamics as a circle of equally spaced balls colored black or white, which move in a clockwise direction at the same speed and change color whenever they pass a mark on the circle; that construction is the Kac ring model.
Boltzmann transport equation