  We define the probability structure of a continuous-time time-homogeneous
Markov jump process, on a finite graph, that represents the continuous-time
counterpart of the so-called Ruelle-Bowen discrete-time random walk. It
constitutes the unique jump process having maximal entropy rate. Moreover, it
has the property that, given the number of jumps between any two specified
end-points on the graph, the probability of traversing any one of the
alternative paths that are consistent with the specified number of jumps and
end-points, is the same for all, and thereby depends only on the number of
jumps and the end-points and not the particular path being traversed.
