We give bounds on the exponential decay rate of entropy in the random transposition model and the Bernoulli--Laplace model which are independent of the number of sites and the number of particles. This is then used to give a bound on the time to stationarity in the total variation norm.
"Exponential decay of entropy in the random transposition and Bernoulli-Laplace models." Ann. Appl. Probab. 13 (4) 1591 - 1600, November 2003. https://doi.org/10.1214/aoap/1069786512