Spatial distributions of observables in systems under thermal gradients

The departure behavior of the observables from their thermal equilibrium expectation values was analyzed under heat flow in a steady-state nonequilibrium environment. The relationship between the momentum cumulants and the spatial distribution was also investigated. It was observed that the temperature profile for a given nonequilibrium steady state combined with deviations of physical observables could be used to develop a consistent description of spatial distribution of the observables. The results show that lower order cumulants characterize the difference of the nonequilibrium distribution from the one in local equilibrium.