  In the absence of acceleration, the velocity formula gives "distance
travelled equals speed multiplied by time". For a broad class of Markov chains
such as circulant Markov chains or random walk on complete graphs, we prove a
probabilistic analogue of the velocity formula between entropy and hitting
time, where distance is the entropy of the Markov trajectories from state $i$
to state $j$ in the sense of [L. Ekroot and T. M. Cover. The entropy of Markov
trajectories. IEEE Trans. Inform. Theory 39(4): 1418-1421.], speed is the
classical entropy rate of the chain, and the time variable is the expected
hitting time between $i$ and $j$. This motivates us to define new entropic
counterparts of various hitting time parameters such as average hitting time or
commute time, and prove analogous velocity formulae and estimates between these
quantities.
