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A systematic analysis of thermodynamic properties performed on Ce-baseexemplary compounds allows to identify different types of behaviors as thesystem approaches the quantum critical region. They are recognized in therespective magnetic phase boundaries (T_{N,C}(x)) as a change from theclassical negative curvature to a linear composition ($x$) dependence, theoccurrence of a critical point or the evanescence at finite temperature underpressure at finite temperature. In the first case, an anomalous reduction ofthe entropy S_m respect to the S_m = RLn2 value (expected for the usualCe-magnetic doublet ground state) is observed around x_{cr}, and analyzedtaking profit of detailed studies performed on CeIn_{3-x}Sn_x alloys. Asexpected from Maxwell relations, the volume variation V_0(x) at T=>0 also showsa non-monotonous behavior around x_{cr}.  Different regimes in the entropy variation of the ordered phase (S_{MO}) arerecognized. Only in the former case S_{MO}=> 0 continuously as T_{N,C}=>0,whereas in the second S_{MO}(x,B) remains constant till a first ordertransition occurs. In the third case, the degrees of freedom of the MO phaseare progressively transferred to the heavy fermion component as indicated bythe decreasing C_m(T_N) jump which vanishes at finite temperature.

Atypical thermodynamic behavior of Ce compounds in the vicinity of zero temperature Critical Points