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Second order Boltzmann-Gibbs principle for polynomial functions and applications
In this paper we give a new proof of the second order Boltzmann-Gibbs
principle. The proof does not impose the knowledge on the spectral gap
inequality for the underlying model and it relies on a proper decomposition of
the antisymmetric part of the current of the system in terms of polynomial
functions. In addition, we fully derive the convergence of the equilibrium
fluctuations towards 1) a trivial process in case of supper-diffusive systems,
2) an Ornstein-Uhlenbeck process or the unique energy solution of the
stochastic Burgers equation, in case of weakly asymmetric diffusive systems.
Examples and applications are presented for weakly and partial asymmetric
exclusion processes, weakly asymmetric speed change exclusion processes and
hamiltonian systems with exponential interactions
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