Systems kept out of equilibrium in stationary states by an external source of energy store an energy $Delta U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $Delta U$ for two model systems: ideal gas and Lennard-Jones fluid. $Delta U$ 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 (iii) proportional to the local density. We show that $Delta U /J_U=tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $tau$ is the characteristic time scale of energy outflow from the system immediately after the shutdown of energy flux. We prove that $tau$ is minimized in stable states of the Rayleigh-Benard cell.
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