%0 Journal Article %T Merging for inhomogeneous finite Markov chains, part II: Nash and log-Sobolev inequalities %A L. Saloff-Coste %A J. Z¨²£żiga %J Mathematics %D 2011 %I arXiv %R 10.1214/10-AOP572 %X 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. %U http://arxiv.org/abs/1104.1560v1