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Thermodynamics of irreversible processes — past and present

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References

  • Alsmeyer, H. 1976. Density profiles in argon and nitrogen shock waves measured by the absorption of an electronic beam. J. Fluid Mech. 74: 497–513

    Article  ADS  Google Scholar 

  • Anile, A.M., 1996. Mathematical modelling of charge carrier transport in semiconductors : Problems and Perspectives. Suppl. Rendiconti Circ. Mat. di Palermo, Part. I, Ser. II 45: 27

    MathSciNet  Google Scholar 

  • Au, J. 1998. Flames in extended thermodynamics. Proc. Int. Conf. Waves and Stability in Cont. Mech. Bari. World Scientific Press Singapoor, pp. 27–32

  • Au, J. and L. Wehr. 1997. Light scattering experiment and extended thermodynamics. Contin. Mech. Thermodyn. 9: 155–163

    Article  ADS  Google Scholar 

  • Barbera, E. 1999. On the principle of minimum entropy production for Navier-Stokes-Fourier fluids. Contin. Mech. Thermodyn. : 327–330

  • Barbera, E. and I. Müller. 2006. Inherent frame-dependence of thermodynamic fields in a gas. Acta Mech. 184: 205–216

    Article  MATH  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Bartlmä, F. 1975. Gasdynamik der Verbrennung. Springer, Wien

  • Belousov, B.P. 1958. A periodic reaction and its mechanism. Sbornik referatov po radiacionnojj medicine za 1958. Moscow, pp. 145–147

  • Bénard, H. 1900. Les tourbillons cellulaires dans une nappe liquide. Rev. Gén. Sci. Pure Appl. 11: 1261–1271

    Google Scholar 

  • Bird, G.A. 1970. Aspects of the structure of strong waves. Phys. Fluids 13: 1172–1177

    Article  ADS  Google Scholar 

  • Bird, R.B., H.R. Warner and D.C. Evans. 1971. Kinetic theory and rheology of dumbbell suspensions with Brownian motion. Advances in Polymer Science 8: 1–90

    Article  Google Scholar 

  • Boillat, G. 1965. La propagation des ondes. Gauthier-Villars, Paris, p. 42

  • Boillat, G. 1974. Sur l’existence et la recherche d’équations de conservation supplémentaires pour les systèmes hyperboliques. C.R. Acad. Sci. Paris, Sér. A 278: 909–912

    MATH  MathSciNet  Google Scholar 

  • Boillat, G. and T. Ruggeri. 1997. Moment equations in the kinetic theory of gases and wave velocities. Contin. Mech. Thermodyn. 9: 205–212

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Boltzmann, L. 1868. Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten. Wiener Berichte 58: 517–560

    Google Scholar 

  • Boltzmann, L. 1872. Weitere Studien über das Wärmegleichgewicht zwischen Gasmolekülen, in Sitzungsberichte der Akademie der Wissenschaften Wien Abt. II, pp. 275–370

  • Boltzmann, L. 1886. Der zweite Hauptsatz der mechanischen Wärmetheorie. Lecture given at the ceremony of the Kaiserliche Akademie der Wissenschaften on Math 29th

  • Boltzmann, L. 1896a. Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn E. Zermelo. Ann. Phys. 57: 773–784

    Article  Google Scholar 

  • Boltzmann, L. 1896b. Zu Hrn Zermelos Abhandlung, Über die mechanische Erklärung irreversibler Vorgänge. Ann. Phys. 59: 793–801

    Google Scholar 

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

  • Boltzmann, L. 1904. Über die statistische Mechanik. Lecture given at a scientific meeting in connection with the World Fair in St. Louis. See also E. Broda (1979)

  • Broda, E. 1979. Ludwig Boltzmann, Populäre Schriften. Vieweg Braunschweig

  • Callen, H.B. 1960. Thermodynamics, an introduction to the physical theories of equilibrium thermostatics and irreversible thermodynamics. John Wiley & Sons, New York

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

    Article  ADS  Google Scholar 

  • Cattaneo, C. 1948. Sulla conduzione del calore. Atti del Seminario Matematica Fisico della Università di Modena 3: 83–101

    MathSciNet  Google Scholar 

  • Chapman, S.C. and T.G. Cowling. 1936, 1961. The mathematical theory of non-uniform gases. Cambridge University Press

  • Chen, P. 1973. Growth and decay of waves in solids. in Handbuch der Physik. Springer Heidelberg, Vol. 6A/3

  • Clarke, N.A. 1975. Inelastic light scattering from density fluctuations in dilute gases. The kinetic-hydrodynamic transition in a monatomic gas. Phys. Rev. A 12: 232–244

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  • Clausius, R. 1867. Über den zweiten Hauptsatz der mechanischen Wärmetheorie. Lecture given at the general session of German natural scientists and physicians in Frankfurt/M on September 23rd 1867. Vieweg Braunschweig

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

    ADS  MathSciNet  Google Scholar 

  • Coleman, B.D. and V.J. Mizel. 1964. Existence of caloric equations of state in thermodynamics. J. Chem. Phys. 40: 1116–1125

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Curtiss, C.F., R.B. Bird and O. Hassager. 1976. Kinetic theory and rheology of macromolecular solutions. Adv. Chem. Phys. 35: 31–117

    Article  Google Scholar 

  • de Donder, Th. 1927. L’affinité. Gautier-Villars Paris

  • Dunn, J.E. and R.L. Fosdick. 1974. Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Rational Mech. Anal. 56: 191–252

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Eckart, C. 1940a. The thermodynamics of irreversible processes I : The simple fluid. Phys. Rev. 58: 267–269

    Article  ADS  Google Scholar 

  • Eckart, C. 1940b. The thermodynamics of irreversible processes II : Fluid mixtures. Phys. Rev. 58: 269–275

    Article  ADS  Google Scholar 

  • Eckart, C. 1940c. The thermodynamics of irreversible processes III : Relativistic theory of the simple fluid. Phys. Rev. 58: 919–924

    Article  ADS  Google Scholar 

  • Edelen, D.G.B. and T.A. McLennan. 1973. Material indifference : A principle or a convenience. Int. J. Eng. Sci. 11: 813–817

    Article  MATH  Google Scholar 

  • Enskog, D. 1917. Kinetische Theorie der Vorgänge in mäßig verdünnten Gasen. Inaugural Dissertation Uppsala, Almquist and Wiksell

  • Ericksen, J.L. 1956. Overdetermination of the speed in rectilinear motionof non-Newtonian fluids. Quarterly of Applied Mathematics 14: 319–321

    MathSciNet  Google Scholar 

  • Ericksen, J.L. 1976. On equations of motion of liquid crystals. Quarterly J. Mech. Appl. Math. 29: 203–208

    Article  MATH  Google Scholar 

  • Ericksen, J.L. 1991. Introduction to the thermodynamics of solids. Chapman & Hall, London

  • Feinberg, M. 1979. Lectures on chemical reaction networks. Mathematical Research Center, University of Wisconsin

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

    Article  Google Scholar 

  • Fisher, A. and P.D. Marsden. 1972. The Einstein evolution equations as a first order quasi-linear symmetric hyperbolic system I. Commun. Math. Phys. 28: 1–38

    Article  ADS  Google Scholar 

  • Fourier, J.B.J. 1808. Mémoire sur la propagation de la chaleur dans les corps solides. Nouveau Bulletin des Sciences par la Societé Philomatique de Paris, t. I, n° 6. Paris, Bernard pp. 112–116

  • Fourier, J.B.J. 1822. Théorie analytique de la chaleur. Paris : Firmin Didot Père et Fils

  • Frank, F.C. 1958. On the theory od liquid crystals. Discuss. Faraday Soc. 25: 19–28

    Article  Google Scholar 

  • Friedrichs, K.O. and P.O. Lax. 1971. Systems of conservation laws with a convex extension. Proc. Natal. Acad Sci. USA 68: 1686–1688

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Fu, S., Y. Huo and I. Müller. 1993. Thermodynamics of pseudoelasticity – an analytical approach. Acta Mech. 99: 1–19

    Article  Google Scholar 

  • de Gennes, P.G. 1974. The Physics of Liquid Crystals. Clarendon Press Oxford

  • Gibbs, J.W. 1875–1878. On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy III. pp. 108–248, Oct. 1875–May 1876, and pp. 342–524, May 1877–July 1878

  • Giesekus, H. 1956. Das Reibungsgesetz der strukturviskosen Flüssigkeit. Kolloid-Zeitschr. 147–149: 29–45

    Article  Google Scholar 

  • Giesekus, H. 1958. Die rheologische Zustandsgleichung. Rheol. Acta 1: 2–20

    Article  Google Scholar 

  • Glansdorff, P. and I. Prigogine. 1971. Thermodynamic theory of structure, stability and fluctuations. Wiley-Interscience, London New York

  • Godunov, S.K. 1961. An interesting class of quasi-linear systems. Dokl. Akad. Nauk 139, Soviet Math. 2: 521–523

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Grad, H. 1952. The profile of a steady plane shock wave. Comm. Pure Appl. Math 5: 257–300

    Article  MATH  MathSciNet  Google Scholar 

  • Grad, H. 1958. Principles of the kinetic theory of rarefied gases. in Handbuch der Physik, Springer Heidelberg, Vol. XII

  • Green, W.A. 1964. The growth of plane discontinuities propagating into a homogeneous deformed material. Arch. Rational Mech. Anal. 16: 79–88

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Grioli, G. 1979. Sulla propagazione di onde termomechaniche nei continui. Nota I, II Atti Acc. Naz. Lincei 67: 332–339, 426–432

    MATH  MathSciNet  Google Scholar 

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

  • de Groot, S.R. and P. Mazur. 1974. Anwendung der Thermodynamik irreversibler Prozesse. BI-Taschenbuch Nr. 162 Bibliographisches Institut, Mannheim/Wien/Zürich

  • Hackl, K. and F.D. Fischer. 2008. On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials. Proc. R. Soc. A 464: 117–132

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Hemmer, P.C. 1959. Dynamic and stochastic types of motion in the linear chain. Det Fysiske Seminar i Trondheim No. 2

  • Hirschfelder, J.O., C.F. Curtiss and D.E. Campbell. 1953. The theory of flame propagation IV. J. Phys. Chem. 57: 403–414

    Article  Google Scholar 

  • Holway, L.H. 1964. Existence of kinetic theory solutions to the shock structure problem. Phys. Fluids 7: 911–913

    Article  ADS  MATH  Google Scholar 

  • Joseph, D.D. 1981. Instability of the rest state of fluids of arbitrary grade greater than one. Arch. Rational Mech. Anal. 45: 251–256

    Google Scholar 

  • Jou, D., J. Casas-Vázquez and G. Lebon. 1993. Extended Irreversible Thermodynamics, Springer Heidelberg

  • Kullback, S. and R.A. Leibler. 1951. On information and sufficiency, in Annals of Mathematical Statistics, Vol. 22, pp. 79–86

  • Landau, L.D. 1941. The theory of superfluidity of HeII. J. Phys. (USSR) 5: 71–90

    Google Scholar 

  • Lifschitz, E.M. 1944. Radiation of sound in HeII. J. Phys. (USSR) 8: 110

    Google Scholar 

  • Liu, I-Shih. 1972a. On Irreversible Thermodynamics. Dissertation Johns Hopkins University

  • Liu, I-Shih. 1972b. Method of Lagrange multipliers for the exploitation of the entropy inequality. Arch. Rational Mech. Anal. 46: 131–148

    ADS  MATH  MathSciNet  Google Scholar 

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

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Liu, I-Shih and I. Müller. 1984. Thermodynamics of mixtures of fluids. in Rational Thermodynamics, edited by C. Truesdell, 2nd edn. pp. 264–285

  • Liu, I-Shih, I. Müller and T. Ruggeri. 1986. Relativistic thermodynamics of gases. Ann. Phys. 169: 191–219

    Article  ADS  Google Scholar 

  • Longuet-Higgins, C. and M.E. Fisher. 1991. Lars Onsager 1903–1976. Biographical Memoir. National Academy of Sciences, Washington D.C.

  • Loschmidt, J. 1876. Über den Zustand des Wärmegleichgewichts eines Systems von Körpern mit Rücksicht auf die Schwerkraft. Sitzungsberichte der Akademie der Wissenschaften Wien, Abteilung 2, 73 (1876), p. 128 and 366. Cont’d in 75 (1877), p. 287, and in 76 (1877), p. 209

  • Loschmidt, J. 1865. Zur Grösse der Luftmoleküle. in Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, Wien 52, Abt. II, pp. 395–413

  • Lotka, A.J. 1910. Zur Theorie der periodischen Reaktionen. Z. Phys. Chem. 72: 508–511

    Google Scholar 

  • Magalinskij, V.B. 1959. Dynamical Model in the Theory of the Brownian Motion. Zh. Eksp. Teor. Fiz. 36: 1942–1944 [Soviet Physics JETP 36: 1381–1382]

    Google Scholar 

  • Maxwell, J.C. 1860. Illustrations of the dynamical theory of gases. Phil. Mag. 19: 19–32, cont’d in 20: 21–37

    Google Scholar 

  • Maxwell, J.C. 1879. On Boltzmann’s theorem on the average distribution of energy in a system of material points. Cambridge Philosophical Society’s Transactions XII, pp. 547–570

  • Meixner, J. 1941. Zur Thermodynamik der Thermodiffusion. Ann. Phys. 39: 333–365

    Article  MATH  Google Scholar 

  • Meixner, J. 1943. Zur Theorie der irreversiblen Prozesse. Z. Phys Chem. B 53: 235–263

    Google Scholar 

  • Meixner, J. 1968. TIP has many faces. Proc. IUTAM Symposium Vienna, June 22–28, 1966. Springer Vienna

  • Miller, D.G. 1960. Thermodynamics of irreversible processes; the experimental verification of the Onsager reciprocal relations. Chem. Rev. 15–37

  • Müller, I. 1962. Durch eine äußere Kraft erzwungene Bewegung der mittleren Masse eines linearen Systems von N durch Federn verbundenen Massen. Diploma thesis, Technical University Aachen

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

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

    Article  ADS  MATH  Google Scholar 

  • Müller, I. 1967b. On the entropy inequality. Arch. Rational Mech. Anal. 26: 118–141

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Müller, I. 1968. A thermodynamic theory of mixtures of fluids. Arch. Rational Mech. Anal. 28: 1–39

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Müller, I. 1970. A new systematic approach to non-equilibrium thermodynamics. Pure Appl. Chem. 22: 335–342

    Article  Google Scholar 

  • Müller, I. 1972. On the frame dependence of stress and heat flux. Arch. Rational Mech. Anal. 45: 241–250

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Müller, I. 1973. A new approach to thermodynamics of simple mixtures. Zeitschrift für Naturforschung A 28: 1801–1813

    ADS  Google Scholar 

  • Müller, I. 1979. Stress and heat flux in a dumbbell solution. Archives of Mechanics 31: 233–249

    MATH  Google Scholar 

  • Müller, I. 1999. Speeds of propagation in classical and relativistic extended thermodynamics. http:/www.livingreviews.org/articles/Volume2/1999-1mueller

  • Müller, I. 2007. A history of thermodynamics, the doctrine of energy and entropy. Springer Heidelberg

  • Müller, I. 2010. Thermodynamics and evolutionary genetics. Contin. Mech. Thermodyn. 22: 189–201

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Müller, I. and W.H. Müller. 2009. Fundamentals of thermodynamics and applications, with many citations from Avogadro to Zermelo. Springer Heidelberg

  • Müller, I. and T. Ruggeri. 1993. Extended Thermodynamics. Springer Tracts of Natural Philosophy. Springer New York, Vol. 37

  • Müller, I. and T. Ruggeri. 1998. Rational Extended Thermodynamics. Springer Tracts of Natural Philosophy, 2nd edn., Springer New York, Vol. 37

  • Müller, I. and T. Ruggeri. 2004. Stationary heat conduction in radially symmetric situations. J. Non-Newtonian Fluid Mech. 119: 139–143

    Article  MATH  Google Scholar 

  • Müller, I. and P. Strehlow. 2003. Kinetic temperature and thermodynamic temperature. 8th Temperature Symposium Proceeding. Springer New York

  • Müller, I. and P. Villaggio. 1976. Conditions of stability and wave speeds for fluid mixtures. Meccanica XI: 191–195

    Article  Google Scholar 

  • Müller, I., D. Reitebuch and W. Weiss. 2002. Extended thermodynamics – consistent in order of magnitude. Contum. Mech. Thermodyn. 15: 113–146

    Article  Google Scholar 

  • Navier, L. 1822. Mémoires sur les lois du mouvement des fluids. Mémoires de l’Académie des Sciences VI, pp. 389–440

  • Noll, W. 1958. A mathematical theory of the behaviour of Continuous media. Arch. Rational Mech. Anal. 2: 198–26

    Article  ADS  MathSciNet  Google Scholar 

  • Ohwada, T. 1996. Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures. Finite difference analysis of the non-linear Boltzmann equation for hard-sphere molecules. Phys. Fluid. 15: 2668–2680

    Google Scholar 

  • Oldroyd, J.G. 1950. On the formulation of rheological equations of state. Proc. Roy. Soc. Lond. A 200: 523–541

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Onsager, L. 1931a. Reciprocal relations in irreversible thermodynamics I. Phys. Rev. 37: 405–426

    Article  ADS  Google Scholar 

  • Onsager, L. 1931b. Reciprocal relations in irreversible thermodynamics II. Phys. Rev. 38: 2265–2279

    Article  ADS  MATH  Google Scholar 

  • Oseen, C.W. 1921. Versuch einer kinetischen Theorie der kristallinischen Flüssigkeiten, Gl. Svenska Vetenskapsakademiens Handligar, 61, No. 16

  • Planck, M. 1970. Wissenschaftliche Autobiographie. 5th edn. J.A. Barth, Leipzig

  • Poincaré, H. 1890. Sur le problème des trois corps et les équations de dynamique. Acta Mat. 13: 1–270

    MATH  Google Scholar 

  • Poisson, S.D. 1829. Mémoire sur l’équilibre et le mouvement des corps élastique. MAS 8: 357–570

    Google Scholar 

  • Poisson, S.D. 1831. Mémoires sur les équations générales de l’équilibre et du mouvement des corps solides élastiques et des fluides. Journal de l’École Polytechnique XIII cahier 20: 139–186

    Google Scholar 

  • Prigogine, I. and G. Nicolis. 1977. Self-organization in non-equilibrium systems. John Wiley New York

  • Prigogine, I. and I. Stengers. 1983. Dialog mit der Natur. Neue Wege naturwissenschaftlichen Denkens. Piper München

  • Reitebuch, D. 2005. Konsistent geordnete erweiterte Thermodynamik. Dissertation Technische Universität Berlin

  • Rubin. 1961. Statistical Mechanics of simple cubic lattices. Model for the study of Brownian motion, II. J. Math. Phys. 2: 373–381

    Article  ADS  Google Scholar 

  • Ruggeri and Strumia. 1981. Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics. Ann. Inst. Henri Poincaré 34 A : 65–84

    Google Scholar 

  • Schrödinger, E. 1948. Statistical Mechanics. Cambridge at the University Press

  • Simonsohn, G. 1972. The role of the first order auto-correlation function in conventional grating spectroscopy. Opt. Commun. 5

  • Sommerfeld, A. and H. Bethe. 1956. Elektronentheorie der Metalle. Handbuch der Physik XIV, Springer, Heidelberg

  • Spengler, O. 1917. Der Untergang des Abendlandes. Umrisse einer Morphologie der Weltgeschichte. C.H. Beck München

  • Stefan, J. 1971. Über das Gleichgewicht und die Bewegung, insbesondere die Diffusion von Gasmengen. Wiener Sitzungsberichte 63: 63–124

    Google Scholar 

  • Stokes, G.G. 1845. On the theories of the internal friction of fluids and of the equilibrium and motion of elastic solids. Transactions of the Cambridge Philosophical Society III: 287–305

    Google Scholar 

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

    ADS  Google Scholar 

  • Struchtrup, H. 1991. Der zweite Schall in der Literatur der Festkörperphysik – eine kritische Durchsicht. Diploma thesis, TU Berlin

  • Struchtrup, H. 1996. Zur irreversiblen Thermodynamik der Strahlung. Doctoral dissertation TU. Berlin

  • Struchtrup, H. 1997. An extended moment method in radiative transfer : The matrices of mean absorption and scattering coefficients. Ann. Phys. 257: 111–135

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Struchtrup, H. 1998a. Extended thermodynamics of Radiation, in Rational Extended Thermodynamics, edited by I. Müller, T. Ruggeri, Springer New York, Chap. 13

  • Struchtrup, H. 1998b. Extended Thermodynamicds of Phonons. in Rational Extended Thermodynamics, edited by I. Müller, T. Ruggeri, Springer New York, Chap. 14

  • Struchtrup, H. 2005. Macroscopic Transport Equations for Rarefied Gases – Approximation Methods in the Kinetic Theory. Springer, Heidelberg

  • Thomson, W. 1862. On the secular cooling of the earth. Trans. R. Soc. Edinb. 23: 157–159

    Google Scholar 

  • Torrilhon, M. 1999. Thermodynamische Berechnung der Ausbreitung von Flammen. Diploma thesis Technical University Berlin

  • Truesdell, C. 1965. Elements of Continuum Mechanics. Springer New York

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

  • Truesdell, C. 1968. Sulle basi della termodinamica delle miscele. Rendiconti Accademia Nazionale dei Lincei 8: 44

    Google Scholar 

  • Truesdell, C. 1969. Rational Thermodynamics. McGraw Hill Book Company, New York

  • Truesdell, C. 1976. Correction of two errors in the kinetic theory that have been used to cast unfounded doubt upon the principle of material frame indifference. Meccanica 11: 196–199

    Article  ADS  MATH  Google Scholar 

  • Turner, R.E. 1960. Motion of a heavy particle in a one-dimensional chain. Physica D 26: 269–273

    Google Scholar 

  • Virga, E. 1994. Variational Theories for Liquid Crystals. Chapman & Hall London

  • Volterra, V. 1931. Lecons sur la théorie mathématique de la lutte pour la vie. Gauthier-Villars Paris

  • Waldmann, L. 1958. Transporterscheinungen in Gasen von mittlerem Druck. in Handbuch der Physik, Springer Heidelberg, Vol. XII

  • Weiss, W. 1990. Zur Hierarchie der erweiterten Thermodynamik. Dissertation Technical University Berlin

  • Weiss, W. 1995. Continuous shock structure in extended thermodynamics. Phys. Rev. E Part A 52: 5760–5763

    Article  ADS  Google Scholar 

  • Weiss, W. 1996a. The balance of entropy on earth. Cont. Mech. Thermodyn. 8: 37–51

    Article  Google Scholar 

  • Weiss, W. 1996b. Coments on Existence of kinetic theory solutions to the shock structure problem [Phys. Fluids 7, 911 (1964)] by L.H. Holway. Phys. Fluids 8: 1689–1690

    Google Scholar 

  • Weiss, W. 1998. On the radiative and material entropy production. Proc. IX Int. Conf. on Waves and Stability in Continuous Media. Suppl. Rendiconti Circ. Matematico di Palermo II, 57: 501–506

  • Weiss, W. and I. Müller. 1995b. Light scattering and extended thermodynamics. Cont. Mech. Thermodyn. 7: 123–177

    Article  Google Scholar 

  • Woods, L.C. 1981. The bogus axioms of continuum mechanics. Bull. Math. Appl. 17: 98–102

    MATH  MathSciNet  Google Scholar 

  • Yong, Wen-An. 2007. An interesting class of hyperbolic balance laws. e-print service : http://arxiv.org/pdf/0707.3708.pdf, pp. 1–21

  • Zermelo, E. 1896a. Über einen Satz der Dynamik und die mechanische Wärmetheorie. Ann. Phys. 57: 485–494

    Article  Google Scholar 

  • Zermelo, E. 1896b. Über mechanische Erklärungen irreversibler Vorgänge. Eine Antwort auf Hrn. Boltzmann’s, Entgegnung. Ann. Phys. 59: 392–398

    Google Scholar 

  • Zhapotinsky, A.M. 1964. Periodic liquid phase reactions. Doklady Akademija Nauk SSSR 157: 392–395

    Google Scholar 

  • Ziegler, H. 1977, 1983. An Introduction to Thermodynamics. North Holland Publishing Company, Amsterdam

  • Ziegler, H. and C. Wehrli. 1987. The derivation of constitutive relations from the free energy and their dissipation function. Advances in Applied Mechanics 25: 183–238

    Article  ADS  MATH  MathSciNet  Google Scholar 

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Müller, I., Weiss, W. Thermodynamics of irreversible processes — past and present. EPJ H 37, 139–236 (2012). https://doi.org/10.1140/epjh/e2012-20029-1

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