We study a quantity $\mathcal{ T}$ defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium $U_0$, $\Delta U=U-U_0$ divided by the heat flow $J_{ U}$ going out of the system. A recent study suggests that $\mathcal{ T}$ is minimized in steady states (Phys.Rev.E.99, 042118 (2019)). We evaluate this hypothesis using an ideal gas system with three methods of energy delivery: from a uniformly distributed energy source, from an external heat flow through the surface, and from an external matter flow. By introducing internal constraints into the system, we determine $\mathcal{ T}$ with and without constraints and find that $\mathcal{ T}$ is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows $U=U_0*f(J_U)$. In this context, we discuss natural variables for NESS, define the embedded energy (an analog of Helmholtz free energy for NESS), and provide its interpretation.
Categories: cond-mat.stat-mech