{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:46:15Z","timestamp":1760147175644,"version":"build-2065373602"},"reference-count":97,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T00:00:00Z","timestamp":1673308800000},"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>It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables {xk} by the quantum level composition variables {x\u02dck,j} corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.<\/jats:p>","DOI":"10.3390\/e25010145","type":"journal-article","created":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T02:06:03Z","timestamp":1673402763000},"page":"145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["How Flexible Is the Concept of Local Thermodynamic Equilibrium?"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7537-2827","authenticated-orcid":false,"given":"Vijay","family":"Tangde","sequence":"first","affiliation":[{"name":"Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1484-0591","authenticated-orcid":false,"given":"Anil","family":"Bhalekar","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India"},{"name":"106, Himalaya Prestige, South Ambazari Marg, SBI Colony, Gopal Nagar, Nagpur 440 022, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,10]]},"reference":[{"key":"ref_1","unstructured":"De Groot, S.R., and Mazur, P. (1962). Non-Equilibrium Thermodynamics, North Holland."},{"key":"ref_2","unstructured":"Rasetti, M. (2008). Series on Advances in Statistical Mechanics, World Scientific. [1st ed.]."},{"key":"ref_3","unstructured":"Prigogine, I. (1967). Introduction to Thermodynamics of Irreversible Processes, John Wiley-Interscience."},{"key":"ref_4","unstructured":"Haase, R. (1969). Thermodynamics of Irreversible Processes, Addison-Wesley."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gyarmati, I. (1970). Non-Equilibrium Thermodynamics, Springer.","DOI":"10.1007\/978-3-642-51067-0"},{"key":"ref_6","unstructured":"Garc\u00eda-Col\u00edn, L.S. (1990). Termodin\u00e1mica de Processos Irreversibles, Colecci\u00f3n CBI-UAM."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hillert, M. (2008). Phase Equilibria, Phase Diagrams and Phase Transformations. Their Thermodynamic Basis, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511812781"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1063\/1.331592","article-title":"Optimal Staging of Endoreversible Heat Engines","volume":"53","author":"Rubin","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1002\/anie.201001411","article-title":"Current Trends in Finite-Time Thermodynamics","volume":"50","author":"Andresen","year":"2011","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1103\/PhysRev.91.1505","article-title":"Fluctuations and Irreversible Processes","volume":"91","author":"Onsager","year":"1953","journal-title":"Phys. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rastogi, R.P. (2008). Introduction to Non-Equilibrium Physical Chemistry. Towards Complexity and Non-Linear Sciences, Elsevier.","DOI":"10.1016\/B978-044452188-0.50003-3"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1063\/1.1744264","article-title":"Chemical Equilibrium in Complex Mixtures","volume":"28","author":"White","year":"1958","journal-title":"J. Chem. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2651","DOI":"10.3891\/acta.chem.scand.25-2651","article-title":"Thermodynamic Studies of High Temperature Equilibria. III. SOLGAS, a Computer Program for Calculating the Composition and Heat Condition of an Equilibrium Mixture","volume":"25","author":"Eriksson","year":"1971","journal-title":"Acta Chem. Scand"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0364-5916(91)90030-N","article-title":"SGTE Data for Pure Elements","volume":"15","author":"Dinsdale","year":"1991","journal-title":"Calphad"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0364-5916(02)00037-8","article-title":"THERMO-CALC & DICTRA, Computational Tools For Materials Science","volume":"26","author":"Andersson","year":"2002","journal-title":"Calphad"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"128","DOI":"10.3139\/146.020128","article-title":"Applications of Computational Thermodynamics","volume":"93","author":"Hayes","year":"2002","journal-title":"Z. Metallkd."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s11669-006-9009-2","article-title":"CALPHAD and Phase-Field Modeling: A Successful Liaison","volume":"28","author":"Steinbach","year":"2007","journal-title":"J. Phase Equilibria Diffus."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.commatsci.2015.01.029","article-title":"The Implementation of an Algorithm to Calculate Thermodynamic Equilibria for Multi-Component Systems With Non-Ideal Phases in a Free Software","volume":"101","author":"Sundman","year":"2015","journal-title":"Comput. Mater. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.4322\/2176-1523.1059","article-title":"The Calphad Method and Its Role in Material and Process Development","volume":"13","author":"Kattner","year":"2016","journal-title":"Tecnol. Metal. Mater. Min."},{"key":"ref_21","unstructured":"Kui Liu, Z., and Wang, Y. (2016). Computational Thermodynamics of Materials, Cambridge University Press. [1st ed.]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/j.actamat.2020.08.008","article-title":"Computational Thermodynamics and Its Applications","volume":"200","year":"2020","journal-title":"Acta Mater."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lebon, G., Jou, D., and Casas-V\u00e1zquez, J. (2008). Understanding Non-Equilibrium Thermodynamics. Foundations, Applications, Frontiers, Springer.","DOI":"10.1007\/978-3-540-74252-4"},{"key":"ref_24","unstructured":"Casas-V\u00e1zquez, J., Jou, D., and Lebon, G. (1983, January 26\u201330). Recent developments in nonequilibrium thermodynamics. Proceedings of the Meeting Held at Bellaterra School of Thermodynamics Autonomous University of Barcelona, Bellaterra, Barcelona, Spain."},{"key":"ref_25","first-page":"89","article-title":"Extended Irreversible Thermodynamics Beyond the Linear Regime. A Critical Overview","volume":"16","author":"Uribe","year":"1991","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jou, D., Casas-V\u00e1zquez, J., and Lebon, G. (1996). Extended Irreversible Thermodynamics, Springer. [2nd ed.].","DOI":"10.1007\/978-3-642-97671-1"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1140\/epjh\/e2012-20029-1","article-title":"Irreversible Thermodynamics\u2013Past and Present","volume":"37","author":"Weiss","year":"2012","journal-title":"Eur. Phys. J. H"},{"key":"ref_28","first-page":"200","article-title":"Applications of Extended Thermodynamics to Chemical, Rheological, and Transport Processes: A Special Survey Part I. Approaches and Scalar Rate Processes; and Part II. Vector Transport Processes, Shear Relaxation, and Rheology","volume":"20","author":"Nettleton","year":"1995","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_29","first-page":"1","article-title":"Applications of Extended Thermodynamics to Chemical, Rheological, and Transport Processes: A Special Survey Part III. Wave Phenomena","volume":"21","author":"Nettleton","year":"1996","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1063\/1.1711937","article-title":"Thermodynamics with Internal State Variables","volume":"47","author":"Coleman","year":"1967","journal-title":"J. Chem. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/BF00250984","article-title":"A Condition Equivalent to the Existence of Non-Equilibrium Entropy and Temperature for Materials with Internal Variables","volume":"68","year":"1978","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/BF00503803","article-title":"Entropy of Systems with Internal Variables","volume":"7","author":"Lype","year":"1986","journal-title":"Int. J. Thermophys."},{"key":"ref_33","unstructured":"Bampi, F., and Morro, A. (1983, January 26\u201330). Nonequilibrium Thermodynamics: A Hidden Variable Approach. Proceedings of the Recent Developments in Nonequilibrium Thermodynamics, Barcelona, Spain."},{"key":"ref_34","unstructured":"Muschik, W. (1991). Recent Developments in Micromechanics, Springer. Chapter 2."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1515\/JNETDY.2003.003","article-title":"A Comparative Study of the Coupling of Flow with Non-Fickean Thermodiffusion. Part III: Internal Variables","volume":"28","author":"Lhuillier","year":"2003","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Maugin, G. (1999). The Thermodynamics of Nonlinear Irreversible Behaviors: An Introduction, World Scientific. [1st ed.].","DOI":"10.1142\/3700"},{"key":"ref_37","first-page":"217","article-title":"Thermodynamics with Internal Variables. Part I. General Concepts","volume":"19","author":"Maugin","year":"1994","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_38","first-page":"250","article-title":"Thermodynamics with Internal Variables. Part II. Applications","volume":"19","author":"Maugin","year":"1994","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_39","first-page":"906136","article-title":"A Derivation of the Main Relations of Nonequilibrium Thermodynamics","volume":"2013","author":"Pokrovskii","year":"2013","journal-title":"Int. Sch. Res. Not."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1063\/1.431117","article-title":"A Theory of Spontaneous Fluctuations in Microscopic Systems","volume":"63","author":"Keizer","year":"1975","journal-title":"J. Chem. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5037","DOI":"10.1063\/1.431204","article-title":"Concentration Fluctuations in Chemical Reactions","volume":"63","author":"Keizer","year":"1975","journal-title":"J. Chem. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1679","DOI":"10.1063\/1.432341","article-title":"Dissipation and Fluctuations in Nonequilibrium Thermodynamics","volume":"64","author":"Keizer","year":"1976","journal-title":"J. Chem. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4466","DOI":"10.1063\/1.432072","article-title":"On the Kinetic Meaning of the Second Law of Thermodynamics","volume":"64","author":"Keizer","year":"1976","journal-title":"J. Chem. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4431","DOI":"10.1063\/1.432977","article-title":"Fluctuations, Stability, and Generalized State Functions at Nonequilibrium Steady States","volume":"65","author":"Keizer","year":"1976","journal-title":"J. Chem. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2609","DOI":"10.1063\/1.436908","article-title":"Thermodynamics at Nonequilibrium Steady States","volume":"69","author":"Keizer","year":"1978","journal-title":"J. Chem. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1021\/ar50139a004","article-title":"Nonequilibrium Thermodynamics and the Stability of States Far from Equilibrium","volume":"12","author":"Keizer","year":"1979","journal-title":"Acc. Chem. Res."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1103\/PhysRevA.30.1115","article-title":"Reversibility, Work, and Heat at Nonequilibrium Steady States","volume":"30","author":"Keizer","year":"1984","journal-title":"Phys. Rev. A"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2751","DOI":"10.1063\/1.448273","article-title":"Heat, Work, and the Thermodynamic Temperature at Nonequilibrium Steady States","volume":"82","author":"Keizer","year":"1985","journal-title":"J. Chem. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Keizer, J. (1987). Statistical Thermodynamics of Nonequilibrium Processes, Springer.","DOI":"10.1007\/978-1-4612-1054-2"},{"key":"ref_50","first-page":"125","article-title":"The Entropy Dissipation Function","volume":"33","author":"Farkas","year":"1989","journal-title":"Period. Polytech. Bp."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Lucia, U., and Grisolia, G. (2021). Nonequilibrium Temperature: An Approach from Irreversibility. Materials, 14.","DOI":"10.3390\/ma14082004"},{"key":"ref_52","first-page":"209","article-title":"Irreversible Thermodynamic Framework Using Compatible Equations from Thermodynamics and Fluid Dynamics. A Second Route to Generalized Phenomenological Irreversible Thermodynamic Theory (GPITT)","volume":"94","author":"Bhalekar","year":"2002","journal-title":"Bull. Cal. Math. Soc."},{"key":"ref_53","unstructured":"Natarajan, G.S., Bhalekar, A.A., Dhondge, S.S., and Juneja, H.D. (2008). Recent Advances in Thermodynamic Research Including Nonequilibrium Thermodynamics, Proceedings of the 3rd National Conference on Thermodynamics of Chemical and Biological Systems (NCTCBS-2008), Nagpur, India, 16\u201317 October 2008, Department of Chemistry, R. T. M. Nagpur University."},{"key":"ref_54","unstructured":"Bhalekar, A.A. (2011, January 3\u20137). Thermodynamic Insight of Irreversibility. Proceedings of the Third International Conference on Lie-Admissible Treatment of Irreversible Processes (ICLATIP-3), Dhulikhel, Nepal."},{"key":"ref_55","unstructured":"Chapman, S., and Cowling, T.G. (1970). Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, Cambridge University Press. [3rd ed.]."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1515\/jnet-2020-0007","article-title":"The Ideal Gas in Slow Time","volume":"46","author":"Essex","year":"2021","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_57","unstructured":"Liboff, R.L. (2003). Kinetic Theory: Classical, Quantum, and Relativistic Descriptions, Springer. [3rd ed.]. Graduate Texts in Contemporary Physics."},{"key":"ref_58","first-page":"120005-1","article-title":"Nonequilibrium velocity distribution in steady regular shock-wave reflection","volume":"2132","author":"Bondar","year":"2019","journal-title":"AIP Conf. Proc."},{"key":"ref_59","unstructured":"Everett, D.H. (1954). Chemical Thermodynamics, Longmans Green."},{"key":"ref_60","unstructured":"Turro, N.J. (1991). Modern Molecular Photochemistry, University Science Books."},{"key":"ref_61","unstructured":"Rohatgi-Mukherjee, K.K. (1978). Fundamentals of Photochemistry, New Age International."},{"key":"ref_62","unstructured":"Turro, N.J., Ramamurthy, V., and Scaiano, J.C. (2015). Principles of Molecular Photochemistry. An Introduction, University Science Books\/Viva Books Pvt. Ltd.. [Indian ed.]."},{"key":"ref_63","unstructured":"Glasstone, S. (1958). Thermodynamics for Chemists, Princeton\/D. Van Nostrand."},{"key":"ref_64","unstructured":"Pitzer, K.S., and Brewer, L. (1961). Thermodynamics, McGraw-Hill Book Co., Inc.. [2nd ed.]."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/S0069-8040(08)70172-9","article-title":"Experimental Methods for the Study of Fast Reactions","volume":"Volume 1","author":"Hague","year":"1969","journal-title":"Comprehensive Chemical Kinetics"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1021\/ed060p809","article-title":"Electron-Transfer Reactions of Excited States","volume":"60","author":"Sutin","year":"1983","journal-title":"J. Chem. Educ."},{"key":"ref_67","unstructured":"Denbigh, K.G. (1973). The Principles of Chemical Equilibrium, Cambridge University Press."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Jordan, R.B. (2007). Reaction Mechanisms of Inorganic and Organometallic Systems, Oxford University Press. [3rd ed.].","DOI":"10.1093\/oso\/9780195301007.003.0007"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1246\/bcsj.46.2101","article-title":"Electron-Transfer Kinetics of Transition-metal Complexes in Lower Oxidation States. Part I. Electron Spin Resonance Measurements of the Electron-Exchange Rate between Cr(bipy)31+ and Cr(bipy)3","volume":"46","author":"Saji","year":"1973","journal-title":"Bull. Chem. Soc. Jpn."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s12043-999-0132-6","article-title":"Extended Irreversible Thermodynamics and the Quality of Temperature and Pressure","volume":"53","author":"Bhalekar","year":"1999","journal-title":"Pramana-J. Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1103\/RevModPhys.61.41","article-title":"Heat Waves","volume":"61","author":"Joseph","year":"1989","journal-title":"Rev. Mod. Phys."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1103\/RevModPhys.61.41","article-title":"Addendum to the Paper \u201cHeat Waves\u201d","volume":"61","author":"Joseph","year":"1989","journal-title":"Rev. Mod. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1103\/PhysRev.148.766","article-title":"Solution of Linearized Boltzmann Phonon Equation","volume":"148","author":"Guyer","year":"1966","journal-title":"Phys. Rev."},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Straughan, B. (2011). Heat Waves, Springer. [1st ed.].","DOI":"10.1007\/978-1-4614-0493-4"},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Joseph, D.D. (1990). Fluid Dynamics of Viscoelastic Liquids, Springer. [1st ed.].","DOI":"10.1007\/978-1-4612-4462-2"},{"key":"ref_76","first-page":"1293","article-title":"Steady Flows of Slightly Compressible Viscoelastic Fluids of Jeffreys\u2019 Type Around an Obstacle","volume":"16","author":"Talhouk","year":"2003","journal-title":"Differ. Integral Equ."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1140\/epje\/i2005-10016-8","article-title":"A Thin-Film Equation for Viscoelastic Liquids of Jeffreys Type","volume":"17","author":"Rauscher","year":"2005","journal-title":"Eur. Phys. J. E"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"062116","DOI":"10.1103\/PhysRevE.88.062116","article-title":"Local Immobilization of Particles in Mass Transfer Described by a Jeffreys-Type Equation","volume":"88","author":"Rukolaine","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_79","unstructured":"Balescu, R.C. (1975). Equilibrium and Nonequilibrium Statistical Mechanics, Wiley-Interscience; John Wiley and Sons. [1st ed.]."},{"key":"ref_80","first-page":"391","article-title":"The Universe of Operations of Thermodynamics vis-\u00e0-vis Boltzmann Integro-Differential Equation","volume":"77B","author":"Bhalekar","year":"2003","journal-title":"Indian J. Phys."},{"key":"ref_81","unstructured":"Garc\u00eda-Col\u00edn, L.S. (1990). Teor\u00eda Cin\u00e9tica de Los Gases, Universidad Aut\u00f3noma Metropolitana-Iztapalapa. Colecci\u00f3n CBI."},{"key":"ref_82","unstructured":"Lewis, G.N., and Randall, M. (1923). Thermodynamics and the Free Energy of Chemical Substances, McGraw-Hill Publishing Co.. [1st ed.]."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"2300","DOI":"10.1021\/j100539a021","article-title":"Nanosecond Temperature-Jump Technique With an Iodine Laser","volume":"81","author":"Holzwarth","year":"1977","journal-title":"J. Phys. Chem."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"7178","DOI":"10.1021\/j100197a012","article-title":"Applicatlons of Ultrafast Temperature Jump Spectroscopy to Condensed Phase Molecular Dynamics","volume":"96","author":"Chen","year":"1992","journal-title":"J. Phys. Chem."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0009-2614(92)85472-M","article-title":"Multiphonon Up-Pumping and Molecular Hot Spots in Superheated Polymers Studied by Ultrafast Optical Calorimetry","volume":"192","author":"Wen","year":"1992","journal-title":"Chem. Phys. Lett."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"11648","DOI":"10.1021\/j100096a005","article-title":"Energy Flow from Solute to Solvent Probed by Femtosecond IR Spectroscopy: Malachite Green and Heme Protein Solutions","volume":"98","author":"Lian","year":"1994","journal-title":"J. Phys. Chem."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"6338","DOI":"10.1021\/ja0613862","article-title":"Ultrafast T-Jump in Water: Studies of Conformation and Reaction Dynamics at the Thermal Limit","volume":"128","author":"Ma","year":"2006","journal-title":"J. Am. Chem. Soc."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF02845551","article-title":"On the Construction of an Extended Irreversible Thermodynamic Framework for Irreversible Processes","volume":"50","author":"Bhalekar","year":"1998","journal-title":"Pramana-J. Phys."},{"key":"ref_89","first-page":"153","article-title":"On the Generalized Zeroth Law of Thermodynamics","volume":"74B","author":"Bhalekar","year":"2000","journal-title":"Indian J. Phys."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/0020-7225(77)90047-7","article-title":"A Concept of Non-Equilibrium Temperature","volume":"15","author":"Muschik","year":"1977","journal-title":"Int. J. Eng. Sci."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/BF00248902","article-title":"Empirical Foundation and Axiomatic Treatment of Non-Equilibrium Temperature","volume":"66","author":"Muschik","year":"1977","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_92","first-page":"133","article-title":"Non-Equilibrium Contact Quantities and Compound Deficiency at Interfaces Between Discrete Systems","volume":"56","author":"Muschik","year":"2007","journal-title":"Proc.-Est. Acad. Sci. Phys. Math"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"301","DOI":"10.2307\/20023731","article-title":"Reflections on Thermodynamics","volume":"82","author":"Bridgman","year":"1953","journal-title":"Proc. Am. Acad. Arts Sci."},{"key":"ref_94","unstructured":"Bridgman, P.W. (1969). The Nature of Thermodynamics, Peter Smith."},{"key":"ref_95","doi-asserted-by":"crossref","unstructured":"Lucia, U., Grisolia, G., and Kuzemsky, A.L. (2020). Time, Irreversibility and Entropy Production in Nonequilibrium Systems. Entropy, 22.","DOI":"10.3390\/e22080887"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S1355-2198(01)00016-8","article-title":"Bluff Your Way in the Second Law of Thermodynamics","volume":"32","author":"Uffink","year":"2001","journal-title":"Stud. Hist. Phil. Mod. Phys."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1590\/S0103-97331999000100004","article-title":"Entropies Galore!","volume":"29","author":"Landsberg","year":"1999","journal-title":"Braz. J. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/145\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:06:24Z","timestamp":1760119584000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,10]]},"references-count":97,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010145"],"URL":"https:\/\/doi.org\/10.3390\/e25010145","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,1,10]]}}}