Une condition asymptotique pour le calcul de constantes de Sobolev logarithmiques sur la droite.

An explicit formula for the logarithmic Sobolev constant relative to real diffusions or to birth and death integer-valued processes is presented, under an asymptotical assumption for quantities naturally associated to Hardy's inequalities in this context. Taking into account exact comparisons between entropy and appropriate variances, the proof comes back to Poincaré's inequality situation. [ABSTRACT FROM AUTHOR]