Abstract
We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system. Finally, we introduce thermodynamics without time as a primitive concept.
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REFERENCES
N. C. A. da Costa and A. S. Sant'Anna, “The mathematical role of time and spacetime in classical physics,” Found. Phys. Lett. 14, 553–563 (2001).
L. P. Horwitz, R. I. Arshansky, and A. C. Elitzur, Found. Phys. 18, 1159–1193 (1988).
I. Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences (Freeman, San Francisco, 1980).
P. C. W. Davies, About Time: Einstein's Unfinished Revolution (Simon & Schuster, New York, 1995).
A. C. Elitzur and S. Dolev, “Black-hole evaporation entails an objective passage of time,” Found. Phys. Lett. 12, 309–323 (1999).
K. Gödel, in Albert Einstein: Philosopher-Scientist, Vol. II, P. A. Schillip, ed. (Open Court, La Salle, 1949), p. 557.
M. E. Gurtin and W. O. Williams, “An axiomatic foundation for continuum thermodynamics,” Archive for Rational Mechanics and Analysis 26, 83–117 (1967).
A. Padoa, “Essai d'une théorie algébrique des nombres entiers, précédé d'une introduction logique à une théorie déductive quelconque,” Bibliothèque du Congrès International de Philosophie 3, 309–365 (1900).
E. W. Beth, “On Padoa's method in the theory of definition,” Indag. Math. 15, 330–339 (1953).
P. Suppes, Introduction to Logic (Van Nostrand, Princeton, 1957).
A. Tarski, “Some methodological investigations on the definability of concepts,” in Logic, Semantics, Metamathematics, A. Tarski, ed. (Hacket, Indianapolis, 1983), pp. 296–319.
N. Bourbaki, Theory of Sets (Hermann and Addison-Wesley, 1968).
P. Suppes, Set-Theoretical Structures in Science, mimeo (Stanford University, 1967).
N. C. A. da Costa and R. Chuaqui, “On Suppes' set theoretical predicates,” Erkenntnis 29, 95–112 (1988).
R. Carnap, Introduction to Symbolic Logic and Its Applications (Dover, New York, 1958).
E. Mendelson, Introduction to Mathematical Logic (Chapman & Hall, London, 1997).
J. L. Doob, Measure Theory (Springer, New York, 1994).
W. Noll, “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 (North-Holland, Amsterdam, 1959), pp. 266–281.
P. Suppes, “Philosophy and the sciences,” in Acting and Reflecting, W. Sieg, ed. (Kluwer Academic, Dordrecht, 1990), p. 3.
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da Costa, N.C.A., Sant'Anna, A.S. Time in Thermodynamics. Foundations of Physics 32, 1785–1796 (2002). https://doi.org/10.1023/A:1021458908383
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DOI: https://doi.org/10.1023/A:1021458908383