  Recently we have proved NRQCD color octet factorization of S-wave and P-wave
heavy quarkonia production at all orders in coupling constant in QCD in vacuum
at high energy colliders in Eur. Phys. J. C76 (2016) 448 and in
arXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to prove
NRQCD color octet factorization of P-wave heavy quarkonium production in
non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This
proof is necessary to study the quark-gluon plasma at RHIC and LHC.
