The entanglement at finite temperatures is analyzed by using thermal models for colored quarks making up the hadron physical states. We have found that these quantum correlations entirely vanish at {T_c\geq m_q/ ln (1.5)}. For temperatures larger than T_c the correlations are classical. We have also worked out the entanglement for the transverse Ising spin chain. In dependence on both temperature T and transverse field \lambda we can identify a certain region, where the quantum effects are likely to dominate the system. We suggest the mutual information as a quantitative measure for the correlations in the ground state.

PACS numbers: 14.65.-q, 71.45.Gm, 05.70.a