Bounds for the intrinsic viscosity

Lower bound. According to the formalism described in Section 3.7, the intrinsic viscosity [i/] can be calculated in the following way (the shear 

To put this into a variational formulation, we first rewrite eqn (4.169) using the equilibrium distribution function cf f eKp(—U/kBT) and the deviation as 

Since the system is homogeneous, the function satisfies translational invariance i.e., for arbitrary a, 

This condition is needed to ensure that the surface integrals iq pearing in the integral by parts in the following analysis vanish. Substituting eqn (4.171) into eqn (4.169) and retaining the terms linear in k, we have 

Equation (4.177) gives a lower bound for the intrinsib Viscosity. 

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