= Reversible stress of a polar liquid crystal
{title2=$\Sigma^p_{ij}$}
Using the positive <polar molecular field> $h_i=\delta F/\delta p_i$ and <velocity gradient> $\partial_i v_j$, the reversible <order-parameter stress> consists of a distortion contribution and rotational and alignment contributions:
$$
\Sigma^p_{ij}=\Sigma^{(1)}_{ij}
+\frac{p_i h_j-p_jh_i}{2}
+\frac{\xi(p_i h_j+p_jh_i)}2,
\qquad \partial_i\Sigma^{(1)}_{ij}=-p_k\partial_jh_k.
$$
For a local <free-energy density>, a representative is $\Sigma^{(1)}_{ij}=(f-p_kh_k)\delta_{ij}-f_{\partial_i p_k}\partial_jp_k$. The <Euler-Lagrange equation> verifies its <divergence>. <Integration by parts> gives $\delta F=\int\Sigma^p_{ij}\partial_i u_j$ for an incompressible displacement without surface work; the corresponding mechanical power has the opposite sign. <Pressure> contributions may be reassigned in an <incompressible flow>.
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