  In this paper, one investigates the following type of
transportation-information $T_cI$ inequalities: $\alpha(T_c(\nu,\mu))\le
I(\nu|\mu)$ for all probability measures $\nu$ on some metric space $(\XX, d)$,
where $\mu$ is a given probability measure, $T_c(\nu,\mu)$ is the
transportation cost from $\nu$ to $\mu$ with respect to some cost function
$c(x,y)$ on $\XX^2$, $I(\nu|\mu)$ is the Fisher-Donsker-Varadhan information of
$\nu$ with respect to $\mu$ and $\alpha: [0,\infty)\to [0,\infty]$ is some left
continuous increasing function. Using large deviation techniques, it is shown
that $T_cI$ is equivalent to some concentration inequality for the occupation
measure of a $\mu$-reversible ergodic Markov process related to $I(\cdot|\mu)$,
a counterpart of the characterizations of transportation-entropy inequalities,
recently obtained by Gozlan and L\'eonard in the i.i.d. case . Tensorization
properties of $T_cI$ are also derived.
