We determine the logarithmic Sobolev constant for the Bernoulli- Laplace model and the time to stationarity for the symmetric simple exclusion model up to the leading order. Our method for proving the logarithmic Sobolev inequality is based on a martingale approach and is applied to the random transposition model as well. The proof for the time to stationarity is based on a general observation relating the time to stationarity to the hydrodynamical limit.
"Logarithmic Sobolev inequality for some models of random walks." Ann. Probab. 26 (4) 1855 - 1873, October 1998. https://doi.org/10.1214/aop/1022855885