  Entanglement and quantum discord for a pair of nuclear spins $s=1/2$ in a
nanopore filled with a gas of spin-carrying molecules (atoms) are studied. The
correlation functions describing dynamics of dipolar coupled spins in a
nanopore are found. The dependence of spin-pair entanglement on the temperature
and the number of spins is obtained from the reduced density matrix, which is
centrosymmetric (CS). An analytic expression for the concurrence is obtained
for an arbitrary CS density matrix. It is shown that the quantum discord as a
measure of quantum correlations attains a significant value at low
temperatures. It is shown also that the discord in the considered model has
"flickering" character and disappears periodically in the course of the time
evolution of the system. The geometric discord is studied for arbitrary
$4\times 4$ CS density matrices.
