Abstract
We study a quantity defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium , divided by the heat flow going out of the system. A recent study suggests that 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 with and without constraints and find that is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows . 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.
Highlights
The basis of equilibrium thermodynamics relies on the existence of the equilibrium state.The equilibrium state can be characterized by a set of appropriate parameters and some kind of energy-based function of these parameters and internal constraints
We consider an ideal gas driven out-of-equilibrium by three different ways of energy delivery that are common in physical realizations
We use the ideal gas model with three different energy delivery methods to test the hypothesis that ∆U/JU is minimized in steady states
Summary
The basis of equilibrium thermodynamics relies on the existence of the equilibrium state. A prerequisite for any system to become non-equilibrium is a continuous energy flow. There is no systematic approach for dealing with NESS Attempts to create such approaches include: minimum/maximum entropy production principle [2], steady state thermodynamics [3], and driven lattice gas systems [4]. In information theoretical techniques and extended thermodynamics, the heat flow appears as a natural thermodynamic variable in non-equilibrium steady states. Is shown to be minimized in steady states for three different systems [13] This quantity has the dimension of time. The local temperature is defined from the ideal gas law It would be interesting, to consider using effective temperature in non-equilibrium systems and to study their role in energy storage [14,15]
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