  In this paper we study the equilibrium energy fluctuation field of a
one-dimensional reversible non gradient model. We prove that the limit
fluctuation process is governed by a generalized Ornstein- Uhlenbeck process,
which covariances are given in terms of the diffusion coefficient. Adapting the
non gradient method introduced by Varadhan, we are able to derive the diffusion
coefficient. The fact that the conserved quantity (energy) is not a linear
functional of the coordinates of the system, introduces new difficulties of
geometric nature when applying the nongradient method.
