Temperature and correlations in 1-dimensional systems

Local thermodynamic equilibrium(LTE) plays a crucial role in statistical mechanics and thermodynamics. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the systems at hand are represented by the transport coefficients. The robustness and universality of equilibrium properties is not guaranteed in nonequilibrium states, in which different microscopic quantities may behave differently, even if they coincide at equilibrium. We investigate these issues considering 1-dimensional chains of N oscillators. We observe that non-negligible fluctuations, and persistence of correlations frustrate the onset of LTE, hence the existence of thermodynamic fields, such as temperature.