  For discrete-time stochastic processes, there is a close connection between
return/waiting times and entropy. Such a connection cannot be straightforwardly
extended to the continuous-time setting. Contrarily to the discrete-time case
one does need a reference measure and so the natural object is relative entropy
rather than entropy. In this paper we elaborate on this in the case of
continuous-time Markov processes with finite state space. A reference measure
of special interest is the one associated to the time-reversed process. In that
case relative entropy is interpreted as the entropy production rate. The main
results of this paper are: almost-sure convergence to relative entropy of
suitable waiting-times and their fluctuation properties (central limit theorem
and large deviation principle).
