Fluctuation Effects in Smectic Liquid Crystals

Abstract

To describe effects, associated with fluctuations of the macroscopic quantities, we should know their distribution function. As is known (Landau and Lifshits, 1980) this distribution function of any body is proportional to exp S, where

$$ S = \int {{d^3}r\left( {s - \frac{1}{{{T_T}}}E + \frac{{{\mu _T}}}{{{T_T}}}\rho } \right).} $$

(3.1.1)

Here s is the entropy density, E is the energy density, ρ is the mass density of the body, T_T is the temperature of the thermal bath, μ_T is the chemical potential of the thermal bath, and it is asserted here that the thermal bath is at rest (otherwise in (3.1.1) there emerges a term proportional to the velocity of the thermal bath). The quantity S has the meaning of the entropy of a system consisting of a body and thermal bath. The entropy S is a functional of the hydrodynamic variables ϕ _a (r) of the body and achieves its maximum when these variables are equal to their equilibrium values. Then the local temperature and chemical potential of the body are equal to the temperature and chemical potential of the thermal bath and the local velocity is zero.