Derivation of the Balance Laws for Liquid Crystals using Statistical Mechanics
I will outline how one can derive the continuum-level balances for liquid crystals using statistical mechanics. I will start by considering a discrete system of rigid rods, which motivates an appropriate state space. A probability function is then introduced that satisfies the Liouville equation. This equation serves as the starting point for the derivation of all of the continuum-level balances. The terms appearing in the derived balances, some being nonstandard, are interpreted as expected values.