  In this article, using a known method, a computation is performed of the
derivatives of the microcanonical entropy, with respect to the energy up to the
4-th order, using a Laplace transform technique, and adapted it to the case
where the total momentum is conserved. The outcome of this computation answers
a theoretical question concerning the description of thermodynamics associated
with a Hamiltonian flow in presence of an additional conserved quantity besides
energy. This is also of practical interest in numerical simulations of the
microcanonical thermodynamics associated to classical Hamiltonian flows.
