We study a quantity T defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium U0, ΔU=U−U0 divided by the heat flow JU going out of the system. A recent study suggests that 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 T with and without constraints and find that T is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows U=U0∗f(JU). 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.

中文翻译：

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受约束的非平衡系统中的能量存储

我们研究了定义为能量 U 的量 T，它存储在非平衡稳态 (NESS) 中超过其在平衡 U0 中的值，ΔU=U−U0 除以流出系统的热流 JU。最近的一项研究表明，T 在稳态下最小化 (Phys.Rev.E.99, 042118 (2019))。我们使用具有三种能量传递方法的理想气体系统来评估这一假设：来自均匀分布的能源、来自通过表面的外部热流和来自外部物质流。通过将内部约束引入系统，我们确定了有约束和无约束的 T，并发现对于无约束的 NESS，T 是最小的。我们发现所研究的 NESS 中内能的形式遵循 U=U0∗f(JU)。在这种情况下，我们讨论 NESS 的自然变量，