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Early history of extended irreversible thermodynamics (1953–1983): An exploration beyond local equilibrium and classical transport theory

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Abstract

This paper gives a historical account of the early years (1953–1983) of extended irreversible thermodynamics (EIT). The salient features of this formalism are to upgrade the thermodynamic fluxes of mass, momentum, energy, and others, to the status of independent variables, and to explore the consistency between generalized transport equations and a generalized version of the second law of thermodynamics. This requires going beyond classical irreversible thermodynamics by redefining entropy and entropy flux. EIT provides deeper foundations, closer relations with microscopic formalisms, a wider spectrum of applications, and a more exciting conceptual appeal to non-equilibrium thermodynamics. We first recall the historical contributions by Maxwell, Cattaneo, and Grad on generalized transport equations. A thermodynamic theory wide enough to cope with such transport equations was independently proposed between 1953 and 1983 by several authors, each emphasizing different kinds of problems. In 1983, the first international meeting on this theory took place in Bellaterra (Barcelona). It provided the opportunity for the various authors to meet together for the first time and to discuss the common points and the specific differences of their previous formulations. From then on, a large amount of applications and theoretical confirmations have emerged. From the historical point of view, the emergence of EIT has been an opportunity to revisit the foundations and to open new avenues in thermodynamics, one of the most classical and well consolidated physical theories.

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References

  • Alts, T. and I. Müller. 1972. Relativistic thermodynamics of simple heat conducting fluids. Arch. Rat. Mech. Anal. 48: 245–273.

    MATH  Google Scholar 

  • Alvarez, F.X., A.V. Cimmelli, D. Jou and A. Sellitto. 2012. A mesoscopic description of boundary effects in nanoscale heat transport. Nanoscale Syst. MMTA 1: 112–142.

    MATH  Google Scholar 

  • Anile, A.M. and S. Pluchino. 1984. Linear waves modes for dissipative fluids with rate type constitutive equations. Meccanica 19: 204–110.

    Google Scholar 

  • Arnold, V. 1966. Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16: 319–361.

    Google Scholar 

  • Bampi, F. and A. Morro. 1984. Non equilibrium thermodynamics: a hidden variable theory. In: Lecture Notes in Physics, Vol. 199. Springer, Berlin.

  • Barbera, E., I. Müller, D. Reitebuch and N.R. Zhao. 2004. Determination of boundary conditions in extended thermodynamics via fluctuation theory. Continuum Mech. Thermodyn. 16: 411–425.

    MATH  ADS  Google Scholar 

  • Belinskii, V.A., S. Nikomarov and I.S Khalatnikov. 1979. Investigation of the cosmological evolution of a viscoelastic matter with causal thermodynamics. Sov. Phys. JETP 50: 213–221.

    ADS  Google Scholar 

  • Belousov B.P. 1958. A periodic reaction and its mechanism. Shornik Referatov po Radiacionnoii Medicine za. (Collection of Abstracts on Radiation Medicine), pp. 145–147. Moscow.

  • Bénard, H. 1900. Les tourbillons cellulaires dans une nappe liquide transportant la chaleur par conduction en régime permanent. Rev. Gén. Sci. Pures et Appliquées 11: 1261–1271.

    Google Scholar 

  • Beris, A.N. and B.J. Edwards. 1994. Thermodynamics of Flowing Systems with Internal Microstructures. Oxford Sci. Pub., Oxford.

  • Bird, R.B., C.F. Curtiss, R.C. Armstrong and D. Hassager. 1987. Dynamics of Polymer Liquids, 2nd edition, Vol. 2. Wiley, New York.

  • Boltzmann, L. 1872. Weiteren Studien über das Wärmegleichgewicht zwischen Gasmolekülen. Sitzungsberichte der Akad. der Wissensch. Wien Abt. II: 275–370.

    Google Scholar 

  • Boltzmann, L. 1895, 1898. Vorlesungen über Gastheorie I und II. Verlag Metzger und Wittig, Leipzig.

  • Bubnov, V.A. 1976. Wave concepts in the theory of heat. Int. J. Heat Mass Transfer 19: 175–184.

    MATH  ADS  Google Scholar 

  • Carnot, S. 1824. Réflexions sur la puissance motrice du feu et sur des machines propres à développer cette puissance. Librairie Bachelier, Paris.

  • Casas-Vazquez, J., D. Jou and G. Lebon. (eds.). 1984. Recent Developments in Non- Equilibrium Thermodynamics. In: Lecture Notes in Physics, Vol. 199. Springer, Berlin.

  • Casas-Vazquez, J. and D. Jou. 2003. Temperature in nonequilibrium states: a review of open problems and current proposals. Rep. Prog. Phys. 66: 1937–2023.

    ADS  Google Scholar 

  • Casimir, H.B.G. 1945. On Onsager’s principle of microscopic irreversibility. Rev. Mod. Phys. 17: 343–350.

    ADS  Google Scholar 

  • Cattaneo, C. 1948. Sulla conduzione del calore. Atti Seminario Mat. Fis. Univ. Modena 3: 83–101.

    MathSciNet  Google Scholar 

  • Chapman, S. and T.G. Cowling. 1970. The Mathematical Theory of Non-uniform Gases. Cambridge Univ. Press, Cambridge.

  • Chester, M. 1963. Second sound in solids. Phys. Rev. 131: 2013–2015.

    ADS  Google Scholar 

  • Chester, M. 1966. High-frequency thermometry. Phys. Rev. 145: 76–80.

    MathSciNet  ADS  Google Scholar 

  • Cimmelli, A., D. Jou, T. Ruggeri and P. Van. 2014. Entropy principle and recent results in non-equilibrium theories. Entropy 16: 1756–1807.

    MathSciNet  ADS  Google Scholar 

  • Clausius, R. 1854. Über eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie. Poggendorff’s Annalen der Physik 93: 481–506.

    ADS  Google Scholar 

  • Clausius, R. 1865. Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. Poggendorf’s Annalen der Physik 125: 353–400.

    ADS  Google Scholar 

  • Clebsch, A. 1859. Über die Integration der hydrodynamischen Gleichungen. J. Reine Angew. Math. 56: 1–10.

    MATH  MathSciNet  Google Scholar 

  • Coleman, B.D. and C. Truesdell. 1960. On the reciprocal relations of Onsager. J. Chem. Phys. 33: 28–31.

    MathSciNet  ADS  Google Scholar 

  • Coleman, B.D. and W. Noll. 1963. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rat. Mech. Anal. 13: 167–178.

    MATH  MathSciNet  Google Scholar 

  • Coleman, B.D. 1964. Thermodynamics of materials with memory. Arch. Rat. Mech. Anal. 17: 1–46.

    Google Scholar 

  • Coleman, B.D. and M.E. Gurtin. 1967. Thermodynamics with internal state variables. J. Chem. Phys. 47: 597–613.

    ADS  Google Scholar 

  • Courant, R. and D. Hilbert. 1962. Methods of Mathematical Physics. J. Wiley, New York.

  • de Groot, S.R. 1951. Thermodynamics of Irreversible Processes. North-Holland, Amsterdam.

  • de Groot, S.R. and P. Mazur. 1962. Non-equilibrium Thermodynamics. North-Holland, Amsterdam.

  • Denbigh, R.G. 1950. The Thermodynamics of the Steady state. Wiley, New York.

  • Dufour, L. 1873. Über die Diffusion der Gase durch poröse Wände und die sie begleitenden Termperaturveränderungen. Ann. der Phys. 148: 490–492 (translated from the original article published in French in Arch. Sci. Phys. Nat. Genève 45: 9–11).

    ADS  Google Scholar 

  • Eckart, C. 1940. The thermodynamics of irreversible processes. Phys. Rev. 58: 267–269 and 58: 269–275.

    ADS  Google Scholar 

  • Eu, B.C. 1980. A modified moment method and irreversible thermodynamics. J. Chem.Phys. 73: 2958–2969.

    MathSciNet  ADS  Google Scholar 

  • Eu, B.C. 1992. Kinetic Theory and Irreversible Thermodynamics. Wiley, New York.

  • Fick, A. 1855. Über Diffusion. Ann. Phys. 94: 59–86.

    Google Scholar 

  • Finlayson, B. 1972. The Method of Weighted Residuals and Variational Principles. Acad. Press, New York.

  • Fourier, J.B. 1822. Théorie Analytique de la Chaleur. F. Didot, Paris.

  • Garcia-Colin, L.S. and M. Lopez de Haro. 1982. The Burnett equations in extended irreversible thermodynamics. J. Non-Equilib. Thermodyn. 7: 95–104.

    MATH  ADS  Google Scholar 

  • Garcia-Colin, L.S., R.F. Rodriguez, M. Lopez de Haro, D. Jou and J. Casas-Vazquez. 1984. On the foundations of extended irreversible thermodynamics. J. Stat. Phys. 17: 465–484.

    MathSciNet  ADS  Google Scholar 

  • Garcia-Colin, L.S. and R.F. Rodriguez. 1988a. On the relationship between extended thermodynamics and the wave approach in thermodynamics. J. Non-Equilib. Thermodyn. 13: 81–94.

    MATH  ADS  Google Scholar 

  • Garcia-Colin, L.S. 1988b. Extended non-equilibrium thermodynamics, scope and limitations. Rev. Mexicana Fisica 34: 344–366.

    Google Scholar 

  • Garcia-Colin, L.S. 1995. Extended irreversible thermodynamics: an unfinished task. Mol. Phys. 86: 697–706.

    ADS  Google Scholar 

  • Gaspard, P. 1998. Chaos, Scattering and Statistical Mechanics. Cambridge Univ. Press, Cambridge.

  • Gibbs, W. 1875, 1878. On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy, pp. 108–248 and pp. 342–524.

  • Glansdorff, P. and I. Prigogine. 1964. On a general evolution criterion in macroscopic physics. Physica. 30: 351–374.

    MathSciNet  ADS  Google Scholar 

  • Glansdorff, P. and I. Prigogine. 1971. Thermodynamics of Structures, Stability and Fluctuations. Wiley, New York.

  • Grad, H. 1949. On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2: 331–407.

    MATH  MathSciNet  Google Scholar 

  • Grad, H. 1958. Principles of the kinetic theory of gases. In: Flugge S. (ed.) Hd. der Physik, Vol. XII. Springer, Berlin.

  • Griffin, J.J. and K.K. Kan. 1976. Colliding heavy ions: nuclei as dynamical fluids. Rev. Mod. Phys. 48: 467–477.

    ADS  Google Scholar 

  • Grmela, M. and C. Lye. 1987. Shear flow induced structural changes in polymeric liquid crystals. Phys. Lett. A 120: 282–285.

    ADS  Google Scholar 

  • Grmela, M. 1984. Particle and bracket formulation of kinetic equations. Contemp. Math. AMS 28: 125–132.

    MATH  MathSciNet  Google Scholar 

  • Grmela, M. and G. Lebon 1990. Hamiltonian extended thermodynamics. J. Phys. A23: 3341–3351.

    MathSciNet  ADS  Google Scholar 

  • Grmela, M. 2010. Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering. Adv. Chem. Eng. 36: 75–128.

    Google Scholar 

  • Grmela, M. 2014. Contact geometry of mesoscopic thermodynamics and dynamics. Entropy 16: 1652–1686.

    MathSciNet  ADS  Google Scholar 

  • Gurtin, M.E. and A.C Pipkin. 1968. A general theory of heat conduction with finite wave speed. Arch. Rational Mech. Anal. 31: 116–126.

    MathSciNet  ADS  Google Scholar 

  • Guyer, R.A. and J.A. Krumhansl. 1966. Solution of the linearized Boltzmann phonon equation. Phys. Rev. 148: 766–778 and 148: 778–788.

    ADS  Google Scholar 

  • Gyarmati, I. 1970. Non-equilibrium Thermodynamics. Springer, Berlin.

  • Gyarmati, I. 1977. On the wave approach of thermodynamics and some problems of non- linear theories. J. Non-Equilib. Thermodyn. 2: 233–260.

    MATH  ADS  Google Scholar 

  • Haase, R. 1969. Thermodynamics of Irreversible Processes. Addison-Wesley, Reading MA.

  • Hand, G.L. 1962. A theory of anisotropic fluids. J. Fluid. Mech. 13: 33–46.

    MATH  MathSciNet  ADS  Google Scholar 

  • Hess, S. 1977. On nonlocal constitutive relations, continued fraction expansion for the wave vector dependent diffusion coefficient. Z. Naturforsch. 32a: 678–684.

    MathSciNet  ADS  Google Scholar 

  • Hiscock, W.A. and L. Lindblom. 1985. Generic instabilities in first-order dissipative relativistic fluids theories. Phys. Rev. D 31: 725–733.

    MathSciNet  ADS  Google Scholar 

  • Hutter, K. 1977. The foundations of thermodynamics, its basic postulate and implications. A review of modern thermodynamics. Acta Mechanica 27: 1–54.

    MathSciNet  ADS  Google Scholar 

  • Hutter, K. and I. Müller. 1975. On mixture of relativistic fluids. Helvetica Physica Acta 48: 1–24.

    Google Scholar 

  • Israel, W. 1976. Non stationary irreversible thermodynamics: a causal relativistic theory. Ann. Phys. (New York) 100: 310–331.

    MathSciNet  ADS  Google Scholar 

  • Israel, W. and J.M. Stewart. 1979. Transient relativistic thermodynamics and kinetic theory. Ann. Phys. (NY) 118: 341–372.

    MathSciNet  ADS  Google Scholar 

  • Jaynes, E.T. 1963. Information theory and statistical mechanics. In: Statistical Physics (Ford, W.K. ed.). Benjamin, New York.

  • Jou, D., J. Casas-Vazquez and G. Lebon. 1979. A dynamical interpretation of second-order constitutive equations of hydrodynamics. J. Non-Equilib. Thermodyn. 4: 349–362.

    ADS  Google Scholar 

  • Jou, D., J.E. Llebot and J. Casas-Vazquez. 1982. Thermodynamic aspects of non- equilibrium fluctuations. Phys. Rev. A 25: 3277–3281.

    ADS  Google Scholar 

  • Jou, D. 1983. Equacions de Gibbs generalitzades i extensió de la termodinamica de processos irreversibles. Institut d’Estudis Catalans, Barcelona (in Catalan language).

  • Jou, D., J. Casas-Vazquez and G. Lebon. 1993. Extended Irreversible Thermodynamics. First edition. Second edition 1996. Third edition 2001. Fourth edition 2010. Springer, Berlin.

  • Jou, D., J. Casas-Vazquez and M. Criado-Sancho. 2000. Thermodynamics of Fluids under Flow. Second edition 2011. Springer, Berlin.

  • Jou, D., G. Lebon and M. Criado-Sancho. 2010. Variational principles in thermal transport in nanosystems with heat slip flow. Phys. Rev. E 82: 031128.

    ADS  Google Scholar 

  • Jou, D., J. Casas-Vazquez, G. Lebon and M. Grmela. 2005. A phenomenological scaling approach for heat transport in nanosystems. Appl. Math. Lett. 18: 963–967.

    MATH  Google Scholar 

  • Joule, J.P. 1841. On the heat evolved by metallic conductors of electricity, and in the cells of a battery during electrolysis. Phil. Mag. 19: 275.

    Google Scholar 

  • Kestin, J. and J. Bataille. 1980. Thermodynamics of solids. In: Continuum Models of Discrete Systems. University of Waterloo Press, Waterloo.

  • Kirkwood, J.C. 1967. Selected Topics in Statistical Mechanics. Gordon and Breach, New York.

  • Koide, T., G.S. Denicol, P. Mota and T. Kodama. 2007. Relatisvistic dissipative hydrodynamics: a minimal causal theory. Phys. Rev. C 75: 034909.

    ADS  Google Scholar 

  • Kranys, M. 1972. Kinetic derivation of non-stationary general relativistic thermodynamics. Nuovo Cimento B 8: 417–441.

    ADS  Google Scholar 

  • Kranys, M. 1977. Hyperbolic elasticity of dissipative media and its wave propagation modes. J. Phys. A: Math.Gen. 10: 689–709.

    MATH  MathSciNet  ADS  Google Scholar 

  • Kranys, M. 1989. Casual theories of evolution and wave propagation in mathematical physics. Appl. Mech. Rev. 42: 305–322.

    MathSciNet  ADS  Google Scholar 

  • Lambermont, J. and G. Lebon. 1973. On a generalization of the Gibbs equation for heat conduction. Phys. Lett. A 42: 499–500.

    ADS  Google Scholar 

  • Landau, L.D. and E.M. Lifshitz. 1958. Mechanics of Fluids. Addison Wesley, Reading, Mass.

  • Landau, L.D. and E.M. Lifshitz. 1980. Statistical Physics, 3rd edition, Pergamon, Oxford.

  • Lavenda, B. 1979. Thermodynamics of Irreversible Processes. McMillan, London.

  • Lebon, G. and J. Lambermont. 1973. Generalization of Hamilton’s principle to continuous dissipative systems. J. Chem. Phys. 5: 2929–2936.

    MathSciNet  ADS  Google Scholar 

  • Lebon, G. 1978. Derivation of generalized Fourier and Stokes-Newton equations based on the thermodynamics of irreversible processes. Bull. Acad. Roy. Belgique 64: 456–472.

    ADS  Google Scholar 

  • Lebon, G., D. Jou and J. Casas-Vazqez. 1980a. An extension of the local equilibrium hypothesis. J. Phys. A: Math. Gen. 13: 275–290.

    ADS  Google Scholar 

  • Lebon, G. 1980b. Variational Principles in Thermomechanics. In: Recent Developments in Thermomechanics of Solids (Lebon, G. and Perzyna, P. eds.). CISM Courses and Lectures, Vol. 282, pp. 221–415. Springer, Wien, New York.

  • Lebon, G. and A. Cloot. 1989. Propagation of ultrasonic sound waves in dissipative dilute gases and extended irreversible thermodynamics. Wave Motion 11: 23–32.

    MATH  Google Scholar 

  • Lebon, G and P.C. Dauby. 1990. Heat transport in dielectric crystals at low temperature; A variational formulation based on extended irreversible thermodynamics. Phys. Rev. A 42: 4710–4715.

    ADS  Google Scholar 

  • Lebon, G., M. Ruggieri and A. Valenti. 2008a. Extended thermodynamics revisited: renormalized flux variables and second sound in rigid solids. J. Phys. C 20: 025223.

    Google Scholar 

  • Lebon, G., D. Jou and J. Casas-Vazquez. 2008b. Understanding Non-equilibrium Thermodynamics, Foundations, Applications, Frontiers. Springer, Berlin, Heidelberg.

  • Lebon, G. 2014. Heat conduction at micro and nanoscales: a review through the prism of extended irreversible thermodynamics. J. Non-Equilib. Thermodyn. 39: 35–59.

    Google Scholar 

  • Lhuillier, D. 1979. Stress tensor of dilute polymer solutions. Phys. Fluids 22: 2033–2035.

    ADS  Google Scholar 

  • Liu, I.S. 1972. Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Anal. 46: 131–148.

    MATH  Google Scholar 

  • Liu, I.S. and I. Müller. 1983. Extended thermodynamics of classical and degenerate gases. Arch. Rat. Mech. Anal. 83: 285–332.

    MATH  Google Scholar 

  • Liu, I.S., I. Müller and T. Ruggeri. 1986. Relativistic thermodynamics of gases. Ann. Phys. (New York) 169: 191–219.

    ADS  Google Scholar 

  • Luikov, A.V. 1969. Analytical Heat Diffusion Theory. Acad. Press, New York.

  • Luzzi, R., A.R. Vasconcellos, J. Casas-Vázquez, and D. Jou. 1997. Characterization and measurement of a nonequilibrium temperature-like variable in irreversible thermodynamcs. Physica A 234: 699–714.

    ADS  Google Scholar 

  • Luzzi R., A.R. Vasconcellos and J.S. Ramos. 2001. On the statistical foundations of irreversible thermodynamics. Teubner Verlag, Berlin.

  • Luzzi R., A.R. Vasconcellos and J.S. Ramos. 2002. Predictive statistical mechanics: a non-equilibrium ensemble formalism. Kluwer, Dordrecht.

  • Machlup, S. and L. Onsager. 1953. Fluctuations and irreversible process. II Systems with kinetic energy. Phys. Rev. 91: 1512–1515.

    MATH  MathSciNet  ADS  Google Scholar 

  • Mandel, J. 1978. Propriétés Mécaniques des Matériaux. Eyrolles, Paris.

  • Maugin, G. and W. Muschik. 1994. Thermodynamics with internal variables. J. Non- Equilib. Thermodyn. 19: 217–249 and 19: 250–289.

    MATH  ADS  Google Scholar 

  • Maugin, G. 1999. The Thermodynamics of Nonlinear Irreversible Behaviours. World Scientific, Singapore.

  • Maxwell, J.C. 1867. On the dynamical theory of gases. Philos. Trans. Roy. Soc. London, 157: 49–88.

  • Meixner, J. and H.G. Reik. 1959. Thermodynamik der Irreversible Prozesse. In: Handbuch der Physik, Bd 3/ II. Springer, Berlin.

  • Meixner, J. 1968. TIP has many faces. In: Proceed. IUTAM Symposium Vienna, 1966. Springer, Berlin.

  • Meixner, J. 1974. Coldness and temperature, Arch. Rat. Mech. Anal. 3: 281–290.

    Google Scholar 

  • Mongiovi, M.S. 1991. Superfluidity and the entropy conservation in extended thermodynamics. J. Non- Equilib. Thermodyn. 16: 225–239.

    MATH  ADS  Google Scholar 

  • Mongiovi, M.S. 1992. Thermomechanical phenomena in extended thermodynamics of an ideal monatomic superfluid. J. Non-Equilib. Thermodyn. 17: 183–186.

    ADS  Google Scholar 

  • Müller, I. 1966. Zur Ausbreitungsgeschwindigkeit von Störungen in kontinuierlichen Medien. Ph.D. Thesis, Technical University, Aachen.

  • Müller, I. 1967. Zum Paradox der Wärmetheorie. Z. Phys. 198: 329–344.

    MATH  ADS  Google Scholar 

  • Müller, I. 1969. Toward relativistic thermodynamics. Arch. Rat. Mech. Anal. 34: 259–282.

    MATH  Google Scholar 

  • Müller, I. 1970. Die Kälte funktion, eine univeselle Funktion in der Thermodynamik in der viskoser warmeleitender Flüssigkeiten. Arch. Rat. Mech. Anal. 40: 1–36.

    Google Scholar 

  • Müller, I. 1971. The coldness, a universal function in thermoelastic bodies. Arch. Rat. Mech. Anal. 41: 319–332.

    MATH  Google Scholar 

  • Müller, I. and T. Ruggeri. 1993. Extended Thermodynamics. Springer, New York.

  • Müller, I. and Ruggeri, T. 1998. Rational Extended thermodynamics. Springer, New York.

  • Müller, I., D. Reitebuch and W. Weiss. 2003. Extended thermodynamics consistent in order of magnitude. Continuum Mech. Thermodyn. 15: 113–146.

    MATH  ADS  Google Scholar 

  • Müller, I. and W. Weiss. 2012. Thermodynamics of irreversible processes-past and present. Eur. Phys. J. H 37: 139–236.

    Google Scholar 

  • Muschik, W. 1977. Empirical foundation and axiomatic treatment of non-equilibrium temperature. Arch. Rat. Mech. Anal. 66: 379–400.

    MathSciNet  Google Scholar 

  • Muschik, W. 2007. Why so many “Schools” of thermodynamics? Forsch. Ingenieurwes. 71: 149–161.

    Google Scholar 

  • Nettleton, R.E. 1959. Thermodynamics of viscoelasticity in liquids. Phys. Fluids 2: 256–263.

    MATH  MathSciNet  ADS  Google Scholar 

  • Nettleton, R.E. 1960. Relaxation theory of thermal conduction in liquids. Phys. Fluids 3: 216–225.

    MathSciNet  ADS  Google Scholar 

  • Nettleton, R.E. 1984. Early applications of extended irreversible thermodynamics. In: Lecture Notes in Physics, Vol. 199, pp. 1–31. Springer, Berlin.

  • Nettleton, R.E. and S.I Sobolev. 1995. Applications of extended thermodynamics to chemical, rheological, and transport process; a special survey Parts I and II. J. Non-Equilib. Thermodyn. 20: 205–229 and 20: 297–331.

  • Newton, I. 1701. Scala graduum caloris. Calorum descriptions &signa. Phil. Trans. Royal Society London 22: 824–829. English translation in: Newton, I. 1809. Phil. Trans. Royal Society London 4: 572–575.

  • Newton, I. 1726. Philosophiae Naturalis Principia Mathematica, 3rd edition. Londini Juffia Societatis Regis ac Typis.

  • Nicolis, G. and I. Prigogine. 1977. Self-organization in Nonequilibrium Systems. Wiley, New York.

  • Nicolis, G. and I. Prigogine. 1989. Exploring Complexity. Freeman, New York.

  • Noll, W. and C. Truesdell. 1965. The non-linear field theories of mechanics. Springer, New York.

  • Ohm, G.S. 1827. Die galvanische Kette, mathematisch bearbeitet. T.H. Riemann, Berlin.

  • Onsager, L. 1931. Reciprocal relations in irreversible processes. Phys. Rev. 37: 405–426 and 38: 2265–2279.

    ADS  Google Scholar 

  • Öttinger, H.C. 2005. Beyond Equilibrium Thermodynamics. Wiley, Hoboken.

  • Pavon, D., D. Jou and J. Casas-Vazquez. 1980. About the relativistic temperature gradient. Phys. Lett. A 78: 317–318.

    ADS  Google Scholar 

  • Peltier, J.C. 1839. Observations sur les multiplicateurs et sur les piles thermo-électriques. Imprimerie E.J. Bailly, Paris.

  • Prigogine, I. 1947. Etude Thermodynamique des Phénomènes Irréversibles. Desoer, Liège.

  • Prigogine, I. 1961. Introduction to Thermodynamics of Irreversible Processes. Interscience, New York.

  • Prigogine, I. 1980. From Time to Becoming. Time and Complexity in the Physical Sciences. Freeman, San Francisco.

  • Reichl, L.E. 1980. A Modern Course in Statistical Physics. Univ. Texas Press, Austin, Texas.

  • Rubi, M. and J. Casas-Vazquez. 1980. Thermodynamical aspects of micropolar fluids. J. Non-Equilib. Thermodyn. 5: 155–164.

    ADS  Google Scholar 

  • Ruggeri, T. 1993. Recent results on wave propagation in continuous media. In: CISM Courses and Lectures, Vol. 344, pp. 105–154. Springer, Wien, New York.

  • Seebeck, T.J. 1821. Über den Magnetism der Galvanische Kette. K. Akad. Wiss. Berlin.

  • Sieniutycz, S. 1984. Variational approach to extended irreversible thermodynamics of heat and mass transfer. J. Non-Equilib. Thermodyn. 9: 61–71.

    MATH  ADS  Google Scholar 

  • Sieniutycz, S. and P. Salomon. (eds.). 1992. Extended thermodynamics systems. Taylor and Francis, New York.

  • Sieniutycz, S. 1994. Conservation Laws in Variational Thermo-Hydrodynamics. Springer, Berlin.

  • Soret, C. 1879. Sur l’état d’équilibre que prend au niveau de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées à des températures différentes. Arch. Sci. Phys. Nat. Genève 2: 187.

    Google Scholar 

  • Stewart, J.M. 1977. Non-transient relativistic thermodynamics and kinetic theory. Proc. Roy. Soc. London A 357: 59–75.

    ADS  Google Scholar 

  • Stocker, H. and W. Greiner. 1986. High energy heavy ion collisions-probing the equation of state of highly excited hadronic matter. Phys. Rep. 137: 277–392.

    ADS  Google Scholar 

  • Stokes, G.C. 1851. On the effect of the internal friction of fluids on the motion of the pendulums. Transactions of the Cambridge Phil. Soc. IX: 8–106.

    ADS  Google Scholar 

  • Struchtrup, H. 2005. Macroscopic Transport Equations for Rarefied Gas Flows. Springer, Berlin, New York.

  • Thomson, W. 1848. On an absolute thermometric scale founded on Carnot’s theory of the motive power of heat and calculated from Regnault’s observations. Phil. Mag. 33: 313–317.

    Google Scholar 

  • Thomson, W. 1851. On the dynamical theory of heat, with numerical results deduced from Mr Joule’s equivalent of a thermal unit, and M. Regnault’s observations on steam. Transactions of the Royal Society of Edinburgh XX (part II): 261–268 and 289–298.

  • Thomson, W. 1854. Account of experimental investigations to answer questions originating in the mechanical theory of thermoelectric currents. Edinburgh Roy. Soc. Proc. III: 255.

    Google Scholar 

  • Truesdell, C. 1966. Six Lectures on Modern Natural Philosophy. Springer, Heidelberg.

  • Truesdell, C. 1969. Rational Thermodynamics. MacGraw Hill, New York.

  • Truesdell, C. and W. Noll. 1965. The Non-Linear Field Theories. In: Handbuch der Physik, Bd. III/3. Springer, Berlin.

  • Turing, A. 1952. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London B 237: 37–72.

    ADS  Google Scholar 

  • van Kampen, N.G. 1987. Chapman-Enskog as an application of the method for eliminating fast variables. J. Stat. Phys. 46: 709–727.

    MATH  MathSciNet  ADS  Google Scholar 

  • Velasco, R.M. and L.S. Garcia-Colin. 1993. The kinetic foundations of non-local nonequilibrium thermodynamics. J. Non-Equilib. Thermodyn. 18: 157–172.

    MATH  ADS  Google Scholar 

  • Verhas, J. 1983. On the entropy current. J. Non-Equilib. Thermodyn. 8: 201–206.

    ADS  Google Scholar 

  • Vernotte, P. 1958. La véritable équation de la chaleur. Compt. Rend. Acad. Sci. Paris 247: 2103–2107.

    MathSciNet  Google Scholar 

  • Vidal, C., G. Dewel and P. Borkmans. 1994. Au-delà de l’Equilibre. Hermann, Paris.

  • Walgraef, D. 1997. Spatio-Temporal Pattern Formation. Springer, New York.

  • Wei, J. 1966. Irreversible thermodynamics in Engineering. Ind. Eng. Chem. 58: 55–60.

    Google Scholar 

  • Weiss, W. 1990. Hierarchie der Erweiterten Thermodynamik. Dissertation Tech. Univ. Berlin.

  • Wilhelm, H.E. and S.H. Choi. 1975. Nonlinear hyperbolic theory of thermal waves in metals. J. Chem. Phys. 63: 2119–2123.

    MathSciNet  ADS  Google Scholar 

  • Woods, L.C. 1981. The bogus axioms of continuum mechanics. Bull. Inst. Math. Appl. 17: 98–102 and 1982. 18: 64–67.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Département d’Astrophysique, Géophysique et Océanographie, Bâtiment B5, Liège University, 4000, Liège, Belgium

    G. Lebon

  2. Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain

    D. Jou

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  1. G. Lebon
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  2. D. Jou
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Lebon, G., Jou, D. Early history of extended irreversible thermodynamics (1953–1983): An exploration beyond local equilibrium and classical transport theory. EPJ H 40, 205–240 (2015). https://doi.org/10.1140/epjh/e2014-50033-0

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  • DOI: https://doi.org/10.1140/epjh/e2014-50033-0

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