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Storage of Energy in Constrained Non-Equilibrium Systems

Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
Author to whom correspondence should be addressed.
Entropy 2020, 22(5), 557;
Received: 24 April 2020 / Revised: 12 May 2020 / Accepted: 14 May 2020 / Published: 16 May 2020
(This article belongs to the Special Issue Evolution and Thermodynamics)
We study a quantity T defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium U 0 , Δ U = U U 0 divided by the heat flow J U 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 = 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. View Full-Text
Keywords: non-equilibrium stationary states; energy fluxes; internal energy; ideal gas; heat transfer non-equilibrium stationary states; energy fluxes; internal energy; ideal gas; heat transfer
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Zhang, Y.; Giżyński, K.; Maciołek, A.; Hołyst, R. Storage of Energy in Constrained Non-Equilibrium Systems. Entropy 2020, 22, 557.

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