Systems kept out of equilibrium in stationary states by an external source of energy store an energy $\mathrm{\Delta }U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $\mathrm{\Delta }U$ for two model systems: ideal gas and a Lennard-Jones fluid. $\mathrm{\Delta }U$ 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, and (iii) proportional to the local density. We show that $\mathrm{\Delta }U/J_U=\tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $\tau$ is the characteristic timescale 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.

• Received 31 July 2018
• Revised 19 February 2019

DOI:https://doi.org/10.1103/PhysRevE.99.042118