Spectral gap estimates for interacting particle systems via a   Bochner-type identity
  We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice without exclusion, and in the continuum. New estimates for Glauber-type dynamics are also obtained. 
Anne-Severine Boudou, Pietro Caputo, Paolo Dai Pra and Gustavo Posta