Equilibrium fluctuations for a non gradient energy conserving stochastic model
Equilibrium fluctuations | non gradient method | Boltzman-Gibbs principle.
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, whose 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 adapting the non gradient method.