Bound for the spectral gap of a heat conduction model

Consider a linear chain of N particles each carrying an energy. The evolution of the energies is governed by a continuous time, pure jump Markov process. The interactions are nearest neighbor ones preserving the energy. A lower bound (in terms of N), suitable for hydrodynamic limit, is presented for the spectral gap of the Markov generator under the assumption that the stationary distributions are reversible. The work is joint with K. Khanin and D. Szász.