{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:12:29Z","timestamp":1760238749506,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,26]],"date-time":"2020-08-26T00:00:00Z","timestamp":1598400000000},"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 modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye\u2013H\u00fcckel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments hr1\u2026rm(m) by means of the irreducible tensorial Hermite polynomials.<\/jats:p>","DOI":"10.3390\/e22090935","type":"journal-article","created":{"date-parts":[[2020,8,26]],"date-time":"2020-08-26T09:05:37Z","timestamp":1598432737000},"page":"935","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modification of the Electron Entropy Production in a Plasma"],"prefix":"10.3390","volume":"22","author":[{"given":"Juan F.","family":"Garc\u00eda-Camacho","sequence":"first","affiliation":[{"name":"Escuela Superior de F\u00edsica y Matem\u00e1ticas, Instituto Polit\u00e9cnico Nacional, U. P. Adolfo L\u00f3pez Mateos, Zacatenco, M\u00e9xico City C. P. 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7596-2480","authenticated-orcid":false,"given":"Gonzalo","family":"Ares de Parga","sequence":"additional","affiliation":[{"name":"Escuela Superior de F\u00edsica y Matem\u00e1ticas, Instituto Polit\u00e9cnico Nacional, U. P. Adolfo L\u00f3pez Mateos, Zacatenco, M\u00e9xico City C. P. 07738, Mexico"}]},{"given":"Karen","family":"Arango-Reyes","sequence":"additional","affiliation":[{"name":"Escuela Superior de F\u00edsica y Matem\u00e1ticas, Instituto Polit\u00e9cnico Nacional, U. P. Adolfo L\u00f3pez Mateos, Zacatenco, M\u00e9xico City C. P. 07738, Mexico"}]},{"given":"Encarnaci\u00f3n","family":"Salinas-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Escuela Superior de C\u00f3mputo, Instituto Polit\u00e9cnico Nacional, Av. Juan de Dios B\u00e1tiz esq. Av. Miguel Oth\u00f3n de Mendiz\u00e1bal, Col. Lindavista. Del. Gustavo A. Madero., Ciudad de M\u00e9xico C. P. 07738, Mexico"}]},{"given":"Samuel","family":"Dom\u00ednguez-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Unidad Profesional Interdisciplinaria en Ingenier\u00eda y Tecnolog\u00edas Avanzadas Instituto Polit\u00e9cnico Nacional, Av. Miguel Oth\u00f3n de Mendiz\u00e1bal s\/n. Col. La Escalera. U. P. Adolfo L\u00f3pez Mateos, Zacatenco, Del. Gustavo A. Madero, Ciudad de M\u00e9xico C. P. 07738, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1002\/andp.18541691202","article-title":"Ueber eine ver\u00e4nderte Form des zweiten Hauptsatzes der mechanischen W\u00e4rmetheoriein","volume":"93","author":"Clausius","year":"1854","journal-title":"Ann. Phys. Chem."},{"key":"ref_2","unstructured":"Prigogine, I. (1961). Introduction to Thermodynamics of Irreversible Processes, Interscience Publishers. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1103\/RevModPhys.48.239","article-title":"Theory of plasma transport in toroidal confinement systems","volume":"48","author":"Hinton","year":"1976","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","unstructured":"Balescu, R. (1988). Transport Processes in Plasmas, North Holland."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1002\/cpa.3160020403","article-title":"On the kinetic theory of rarefied gases","volume":"2","author":"Grad","year":"1949","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"042103","DOI":"10.1103\/PhysRevE.94.042103","article-title":"Symmetry group and group representations associated with the thermodynamic covariance principle","volume":"95","author":"Sonnino","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_7","first-page":"185","article-title":"Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen","volume":"24","author":"Debye","year":"1923","journal-title":"Phys. Z."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.fluid.2018.01.004","article-title":"The Debye-H\u00fcckel theory and its importance in modeling electrolyte solutions","volume":"462","author":"Kontogeorgis","year":"2018","journal-title":"Fluid Phase Equilib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1021\/j150518a004","article-title":"The Statistical Mechanical Basis of the Debye-H\u00fcckel Theory of Strong Electrolytes","volume":"58","author":"Kirwood","year":"1954","journal-title":"J. Phys. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1119\/1.1969134","article-title":"Plasma Equation of State","volume":"31","author":"Kelly","year":"1963","journal-title":"Am. J. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1119\/1.1970779","article-title":"Remark on the Plasma Equation of State","volume":"32","author":"Wergeland","year":"1964","journal-title":"Am. J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1063\/1.1692223","article-title":"Plasma Virial and Equations of State for a Plasma","volume":"11","author":"Liboff","year":"1968","journal-title":"Phys. Fluids"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"011202","DOI":"10.1103\/PhysRevE.97.011202","article-title":"Measuring the equations of state in a relaxed magnetohydrodynamic plasma","volume":"97","author":"Kaur","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Krall, N.A., and Trivelpiece, A.W. (1973). Principles of Plasma Physics, McGraw-Hill.","DOI":"10.1119\/1.1987587"},{"key":"ref_15","unstructured":"Callen, H. (1985). Thermodynamics and an Introduction to Thermostatistics, John Wiley and Sons."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1515\/jnetdy-2013-0005","article-title":"The principal equations of state for classical particles, photons, and neutrinos","volume":"38","author":"Essex","year":"2013","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Arango-Reyes, K., and Ares de Parga, G. (2020). Completeness of Classical Thermodynamics: The Ideal Gas, the Unconventional Systems, the Rubber Band, the Paramagnetic Solid and the Kelly Plasma. Entropy, 22.","DOI":"10.3390\/e22040398"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1063\/1.872099","article-title":"Transport processes and entropy production in toroidally rotating plasmas with electrostatic turbulence","volume":"4","author":"Sugama","year":"1997","journal-title":"Phys. Plasmas"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"116201","DOI":"10.1088\/0034-4885\/76\/11\/116201","article-title":"Multiscale gyrokinetics for rotating tokamak plasmas: Fluctuations, transport and energy flows","volume":"76","author":"Abel","year":"2013","journal-title":"Rep. Prog. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"082510","DOI":"10.1063\/1.4928101","article-title":"A thermodynamical analysis of rf current drive with fast electrons","volume":"22","author":"Bizarro","year":"2015","journal-title":"Phys. Plasmas"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1088\/0029-5515\/11\/4\/006","article-title":"Penetration of fast hydrogen atoms into a fusion reactor","volume":"11","author":"Riviere","year":"1971","journal-title":"Nucl. Fusion"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1103\/PhysRev.37.405","article-title":"Reciprocal Relations in Irreversible Processes. I","volume":"37","author":"Onsager","year":"1931","journal-title":"Phys. Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"082504","DOI":"10.1063\/1.4960123","article-title":"Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas","volume":"23","author":"Izacard","year":"2016","journal-title":"Phys. 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