We have studied the thermal properties of a peculiar and mysterious reentrant metal-insulator (M-I) transition under delicate pressures on DCNQI-Cu system. The measurements of specific heat and latent heat were carried out by thermal relaxation (0.5 <
T < 40K), adiabatic pulse (20 <
T < 100K) and Differential Thermal Analysis (DTA) methods in the vicinity of the M-I transition controlling the effective pressure. The effective pressure dependence of Sommerfeld constant γ in the metallic phase, temperature dependence of entropy associated with the antiferro-magnetic (AF) ordering of Cu
2+ in the insulator phase and latent heat absorbed or released by crossing the M-I transition give the key information on the reentrant M-I transition. From the experimental results, we estimated the free energy in both phases and confirmed that the competition between the freedom of Cu
2+ spin system and the free electron near the Fermi energy (γ
T term) drives the anomalous reentrant metal-insulator transitions.
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