N2 - We consider a four-level system with two subsystems coupled by weak interaction. The system is in thermal equilibrium. The thermodynamics of the system, namely internal energy, free energy, entropy and heat capacity, are evaluated using the canonical density matrix by two methods. First by Kronecker product method and later by treating the subsystems separately and then adding the evaluated thermodynamic properties of each subsystem. It is discovered that both methods yield the same result, the results obey the laws of thermodynamics and are the same as earlier obtained results. The results also show that each level of the subsystems introduces a new degree of freedom and increases the entropy of the entire system. We also found that the four-level system predicts a linear relationship between heat capacity and temperature at very low temperatures just as in metals. Our numerical results show the same trend. L1 - http://www.journals.pan.pl/Content/94377/PDF/05_paper.pdf L2 - http://www.journals.pan.pl/Content/94377 PY - 2012 IS - No 4 December EP - 108 DO - 10.2478/v10173-012-0029-5 KW - Canonical density matrix KW - Kronecker product KW - Reduced density matrix KW - Entropy A1 - Awoga, Oladunjoye A. A1 - Ikot, Akpan A. A1 - Ituen, Eno E. A1 - Akpabio, Louis E. PB - The Committee of Thermodynamics and Combustion of the Polish Academy of Sciences and The Institute of Fluid-Flow Machinery Polish Academy of Sciences DA - 2012 T1 - Evaluation of the thermodynamics of a four level system using canonical density matrix method SP - 91 UR - http://www.journals.pan.pl/dlibra/publication/edition/94377 T2 - Archives of Thermodynamics