  This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two point space. They appear as local
inequalities of the M/M/$\infty$ queue. They describe in particular the
exponential dissipation of $\Phi$-entropies along this process. This simple
queueing process appears as a model of ``constant curvature'', and plays for
the simple Poisson process the role played by the Ornstein-Uhlenbeck process
for Brownian Motion. Some of the inequalities are recovered by semi-group
interpolation. Additionally, we explore the behaviour of these entropic
inequalities under a particular scaling, which sees the Ornstein-Uhlenbeck
process as a fluid limit of M/M/$\infty$ queues. Proofs are elementary and rely
essentially on the development of a ``$\Phi$-calculus''.
