Flux and storage of energy in nonequilibrium stationary states

Systems kept out of equilibrium in stationary states by an external source of energy store an energy ΔU=U-U_{0}. U_{0} is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine ΔU for two model systems: ideal gas and a Lennard-Jones fluid. ΔU depends not only on the total energy flux, J_{U}, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where the energy flux per unit volume is (i) constant, (ii) proportional to the local temperature, and (iii) proportional to the local density. We show that ΔU/J_{U}=τ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. τ is the characteristic timescale of energy outflow from the system immediately after the shutdown of energy flux. We prove that τ is minimized in stable states of the Rayleigh-Benard cell.