Merging for inhomogeneous finite Markov chains, part II: Nash and   log-Sobolev inequalities
  We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples. 
L. Saloff-Coste, J. Z\'u\~niga
math.PR