  Given an energy potential on the Euclidian space, a piecewise deterministic
Markov process is designed to sample the corresponding Gibbs measure. In
dimension one an Eyring-Kramers formula is obtained for the exit time of the
domain of a local minimum at low temperature, and a necessary and sufficient
condition is given on the cooling schedule in a simulated annealing algorithm
to ensure the process converges to the set of global minima. This condition is
similar to the classical one for diffusions and involves the critical depth of
the potential. In higher dimension a non optimal sufficient condition is
obtained.
