Storage of energy in constrained non-equilibrium systems

Abstract

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 $U=U_0\ast f(J_U)$. 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.

16 pages, 5 figures

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• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Thermal ratchet effect in confining geometries
• Flux and storage of energy in non-equilibrium, stationary states