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References
1822 Fourier, J., Théorie Analytique de la Chaleur. Paris: Didot. See also Oeuvres de Fourier Vol. I, edited by M. G. Darboux. Paris: Gauthier-Villars (1888).
1823 Cauchy, A.-L., Recherches sur l'équilibre et le mouvement intérieur des corps solides ou fluides, élastiques ou non élastiques. Bull. Soc. Philomath. 9. See also Oeuvres de Cauchy (2). Vol. II. Paris: Gauthier-Villars (1958).
1827 Cauchy, A.-L., De la pression ou tension dans un corps solide. Ex. de math. 2, 42. See also Oeuvres de Cauchy (2), Vol. VII Paris: Gauthier-Villars (1889).
1854 Clausius, R., Über eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie. Ann. Physik 93, 481.
1862 Clausius, R., Über die Anwendung des Satzes von der Äquivalenz der Verwandlungen auf die innere Arbeit. Ann. Physik 116, 73.
1865 Clausius, R., Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. Ann. Physik 125, 353.
1868 Fresnel, A., Second supplément au mémoire sur la double réfraction. Oeuvres de Fresnel, Vol. II. Paris: Sénarmont, Verdet, and Fresnel.
1901 Duhem, P., Recherches sur l'hydrodynamique. Ann. Toulouse 3, 315.
1950 Halmos, P. R., Measure Theory. New York: D. Van Nostrand Co.
1956 Ramsey, N. F., Thermodynamics and statistical mechanics at negative absolute temperatures. Phys. Rev. 103, 20.
1957 Preisendorfer, R. W., A mathematical foundation for radiative transfer theory. J. Math. Mech. 6, 685.
1958 Dunford, N., & J. T. Schwartz, Linear Operators, Part I: General Theory. New York: Interscience.
1959 Noll, W., The foundations of classical mechanics in the light of recent advances in continuum mechanics. In: The Axiomatic Method with Special Reference to Geometry and Physics. Amsterdam: North Holland Co. 266.
1960 Truesdell, C., & R. A. Toupin, The Classical Field Theories. In: The Encyclopedia of Physics, Vol. III/1, edited by S. Flügge Berlin-Göttingen-Heidelberg: Springer.
1963 Arens, R., An axiomatic basis for classical thermodynamics. J. Math. Anal. Appl. 6, 207.
1963 Coleman, B. D., & V. J. Mizel, Thermodynamics and departures from Fourier's law of heat conduction. Arch. Rational Mech. Anal. 13, 245.
1963 Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13, 167.
1963 Noll, W., La mécanique classique, basée sur un axiome d'objectivité. La Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles. Colloque International, Paris (1959). Paris: Gauthier-Villars.
1964-1 Coleman, B. D., Thermodynamics of materials with memory. Arch. Rational Mech. Anal. 17, 1.
1964-2 Coleman, B. D., On thermodynamics, strain impulses, and viscoelasticity. Arch. Rational Mech. Anal. 17, 230.
1964 Coleman, B. D., & V. J. Mizel, Existence of caloric equations of state in thermodynamics. J. Chem. Phys. 40, 1116.
1964 Giles, R., Mathematical Foundations of Thermodynamics. New York: Macmillan.
1964 Green, A. E., & R. S. Rivlin, Multipolar continuum mechanics. Arch. Rational Mech. Anal. 17, 113.
1965-1 Gurtin, M. E., Thermodynamics and the possibility of spatial interaction in rigid heat conductors. Arch. Rational Mech. Anal. 18, 335.
1965-2 Gurtin, M. E., Thermodynamics and the possibility of spatial interaction in elastic materials. Arch. Rational Mech. Anal. 19, 339.
1965 Noll, W., The foundations of mechanics. C.I.M.E. Lectures given at the International Mathematical Summer Session, Bressanone, Italy, June 1965. Report 66-2, Department of Mathematics, Carnegie Institute of Technology.
1966-1 Gurtin, M. E., & W. O. Williams, On the inclusion of the complete symmetry group in the unimodular group. Arch. Rational Mech. Anal. 23, 163.
1966-2 Gurtin, M. E., & W. O. Williams, On the Clausius-Duhem inequality. Z. angew. Math. Physik 17, 626.
1966 Wang, C.-C., & R. M. Bowen, On the thermodynamics of non-linear materials with quasi-elastic response. Arch. Rational Mech. Anal. 22, 79.
1967-1 Coleman, B. D., & M. E. Gurtin, Equipresence and constitutive equations for rigid heat conductors. Z. angew. Math. Physik 18, 199.
1967-2 Coleman, B. D., & M. E. Gurtin, Thermodynamics with internal state variables. J. Chem. Phys. Forthcoming.
1967 Coleman, B. D., & V. J. Mizel, Existence of entropy as a consequence of asymptotic stability. Arch. Rational Mech. Anal. 25, 243–270.
1967 Gurtin, M. E., On the thermodynamics of elastic materials. J. Math. Anal. Appl. 18, 38.
1967 Gurtin, M. E., V. J. Mizel, & W. O. Williams, On Cauchy's theorem. Forthcoming.
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Gurtin, M.E., Williams, W.O. An axiomatic foundation for continuum thermodynamics. Arch. Rational Mech. Anal. 26, 83–117 (1967). https://doi.org/10.1007/BF00285676
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DOI: https://doi.org/10.1007/BF00285676