Spatial distributions of observables in systems under thermal gradients

Departures of observables from their thermal equilibrium expectation values are studied under heat flow in steady-state nonequilibrium environments. The relation between the spatial and temperature dependence of these nonequilibrium behaviors and the underlying statistical properties are clarified from general considerations. The predictions are then confirmed in direct numerical simulations within the Fermi-Pasta-Ulam β model. Nonequilibrium momentum distribution functions are also examined and characterized through their cumulants and the properties of higher order cumulants are discussed