Group theoretical statistical mechanics applied to couette flow

Abstract

In group theoretical statistical mechanics (gtsm) the ensemble average is treated with the rules of group theory in the laboratory frame ( X, Y, Z) and the molecule-fixed frame ( x, y, z) of the point group character tables. This allows the determination of non-vanishing averages, such as time correlation functions, at the field-on equilibrium. The effect of couette flow is evaluated on a range of ensemble averages by establishing the symmetry of the strain rate tensor in terms of the irreducible representations of the R h(3) rotation-reflection group in frame ( X, Y, Z). This symmetry, which is also that of the pressure tensor, is D g (0) + D g (1) + D g (2), consisting of an antisymmetric vorticity of symmetry D g (1) and a symmetric strain rate component of general symmetry D g (0) + D g (2). Thus, in addition to ensemble averages of symmetry D g (0) in frame ( X, Y, Z), the applied strain rate tensor allows new ensemble averages of D g (1) symmetry and of D g (0) + D g (2) symmetry. Depending on the number of off-diagonal elements in the strain rate tensor, up to six new elements of time correlation functions of the general type < A ( t) A T(0)> may appear by gtsm in frame ( X, Y, Z), together with new bulk properties whose symmetry is included in D g (0) + D g (1) + D g (2). The latter include thermal conductivity, thermal expansion and electric polarisability. The treatment is extended to the molecule-fixed frame ( x, y, z) using the mapping rules of group theory.