Storage of energy in constrained non-equilibrium systems

TL;DR

This paper investigates the energy storage measure $\u03c4$ in non-equilibrium steady states, demonstrating it is minimized in unconstrained systems and exploring its relation to internal energy and natural variables.

Contribution

It introduces the concept of embedded energy for NESS, evaluates the minimization hypothesis of $\u03c4$, and analyzes energy storage under various constraints and energy delivery methods.

Findings

$\u03c4$ is minimized in unconstrained NESS

Internal energy follows $U=U_0*f(J_U)$ in studied NESS

Embedded energy provides a new thermodynamic potential for NESS

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 $U=U_0*f(J_U)$. 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.