  Thermalization is one of the most important phenomena in statistical physics.
Often, the transition probabilities between different states in the phase space
is or can be approximated by constants. In this case, the system can be
described by Markovian transition kernels, and when the phase space is
discrete, by Markov chains. In this paper, we introduce a macroscopic entropy
on the states of paths of length $k$ and, studying the recursion relation,
obtain a fixed point entropy. This analysis leads to a centrality approach to
Markov chains entropy.
