  We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds.
We provide examples including the Heisenberg group, displacement group, and
Martinet sub-Riemannian structure with arbitrary weighted volumes, in which we
establish analytical bounds for sub-Riemannian curvature dimension bounds and
log-Sobolev inequalities. {These bounds can be used to establish the entropy
dissipation results for sub-Riemannian drift diffusion processes on a compact
spatial domain, in term of $L_1$ distance.} Our derivation of Ricci curvature
is based on generalized Gamma $z$ calculus and $z$--Bochner's formula, where
$z$ stands for extra directions introduced into the sub-Riemannian degenerate
structure.
