{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T19:20:19Z","timestamp":1762543219910,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T00:00:00Z","timestamp":1589587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Polish National Science Centre","award":["Harmonia Grant No. 2015\/18\/M\/ST3\/00403","Sonata Bis Grant No. SONATA BIS DEC- 2017\/26\/E\/ST4\/00041"],"award-info":[{"award-number":["Harmonia Grant No. 2015\/18\/M\/ST3\/00403","Sonata Bis Grant No. SONATA BIS DEC- 2017\/26\/E\/ST4\/00041"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study a quantity    T    defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium     U 0    ,     \u0394 U = U \u2212  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  \u2217 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.<\/jats:p>","DOI":"10.3390\/e22050557","type":"journal-article","created":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T02:43:42Z","timestamp":1589769822000},"page":"557","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Storage of Energy in Constrained Non-Equilibrium Systems"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1608-8302","authenticated-orcid":false,"given":"Yirui","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44\/52, PL-01-224 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3547-1174","authenticated-orcid":false,"given":"Konrad","family":"Gi\u017cy\u0144ski","sequence":"additional","affiliation":[{"name":"Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44\/52, PL-01-224 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2371-4183","authenticated-orcid":false,"given":"Anna","family":"Macio\u0142ek","sequence":"additional","affiliation":[{"name":"Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44\/52, PL-01-224 Warsaw, Poland"},{"name":"Max-Planck-Institut f\u00fcr Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3211-4286","authenticated-orcid":false,"given":"Robert","family":"Ho\u0142yst","sequence":"additional","affiliation":[{"name":"Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44\/52, PL-01-224 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ho\u0142yst, R., and Poniewierski, A. 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