{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:55:32Z","timestamp":1761490532365,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T00:00:00Z","timestamp":1521763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A new model of non-equilibrium thermodynamic states has been investigated on the basis of the fact that all thermodynamic variables can be derived from partition functions. We have thus attempted to define partition functions for non-equilibrium conditions by introducing the concept of pseudo-temperature distributions. These pseudo-temperatures are configurational in origin and distinct from kinetic (phonon) temperatures because they refer to the particular fragments of the system with specific energies. This definition allows thermodynamic states to be described either for equilibrium or non-equilibrium conditions. In addition; a new formulation of an extended canonical partition function; internal energy and entropy are derived from this new temperature definition. With this new model; computational experiments are performed on simple non-interacting systems to investigate cooling and two distinct relaxational effects in terms of the time profiles of the partition function; internal energy and configurational entropy.<\/jats:p>","DOI":"10.3390\/e20040218","type":"journal-article","created":{"date-parts":[[2018,3,27]],"date-time":"2018-03-27T23:37:17Z","timestamp":1522193837000},"page":"218","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Partition Function and Configurational Entropy in Non-Equilibrium States: A New Theoretical Model"],"prefix":"10.3390","volume":"20","author":[{"given":"Akira","family":"Takada","sequence":"first","affiliation":[{"name":"Innovative Technology Research Center, Asahi Glass Co. Ltd., Yokohama 221-8755, Japan"},{"name":"Department of Earth Sciences, University College London, London WC1E 6BT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reinhard","family":"Conradt","sequence":"additional","affiliation":[{"name":"Glass and Composites and Institute of Mineral Engineering, RWTH Aachen University, 52064 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Richet","sequence":"additional","affiliation":[{"name":"Institut de Physique du Globe de Paris, 1 Rue Jussieu, 75005 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gutzow, I., and Schmelzer, J.W.P. (2013). The Vitreous State: Thermodynamics, Structure Rheology, and Crystallization, Springer.","DOI":"10.1007\/978-3-642-34633-0"},{"key":"ref_2","unstructured":"Nemilov, S.V. (1994). Thermodynamic and Kinetic Aspects of the Vitreous State, CRC Press."},{"key":"ref_3","unstructured":"De Donder, T., and van Rysselberghe, P. (1936). Thermodynamic Theory of Affinity: A Book of Principles, Stanford University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1016\/j.jnoncrysol.2010.11.111","article-title":"On the dependence of the properties of glasses on cooling and heating rates: I. Entropy, entropy production, and glass transition temperature","volume":"357","author":"Tropin","year":"2011","journal-title":"J. Non-Cryst. Solids"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1111\/j.1151-2916.1946.tb11592.x","article-title":"Relation between Inelastic Deformability and Thermal Expansion of Glass in its Annealing Range","volume":"29","author":"Tool","year":"1946","journal-title":"J. Am. Ceram. 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