We prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter $L$ may depend on $L$ but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as the square of $L$, that is presented in a forthcoming paper.
"Logarithmic Sobolev Inequality for Zero--Range Dynamics: Independence of the Number of Particles." Electron. J. Probab. 10 525 - 576, 2005. https://doi.org/10.1214/EJP.v10-259