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It is an experimental fact that in a nonequilibrium steady state local thermodynamic variables generically have long range space correlations. We analyse this phenomenon in microscopic models admitting a hydrodynamic scaling limit. The non equilibrium free energy is the Legendre transform of the generating functional of correlation functions and obeys a Hamilton-Jacobi equation from which equations can be derived for correlations of any order. As an example we discuss the two point correlation for arbitrary transport coefficients, external fields and boundary reservoirs. In particular we establish a criterion to determine whether the local thermodynamic variables are positively or negatively correlated in terms of properties of the transport coefficients. Long range space correlations can appear also in equilibrium states if the microscopic dynamics violates time reversal in a "sufficiently strong" way. |
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