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Infinite Systems in SM Explanations: Thermodynamic Limit, Renormalization (semi-) Groups, and Irreversibility

Published online by Cambridge University Press:  01 April 2022

Chuang Liu
Chuang Liu*
Affiliation:
University of Florida
*
†Send requests for reprints to the author, Department of Philosophy, University of Florida, 330 Griffin-Floyd Hall, P.O. Box 118545, Gainesville, FL 32611–8545; e-mail: cliu@phil.ufl.edu.
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Abstract

This paper examines the justifications for using infinite systems to ‘recover’ thermodynamic properties, such as phase transitions (PT), critical phenomena (CP), and irreversibility, from the micro-structure of matter in bulk. Section 2 is a summary of such rigorous methods as in taking the thermodynamic limit (TL) to recover PT and in using renormalization (semi-) group approach (RG) to explain the universality of critical exponents. Section 3 examines various possible justifications for taking TL on physically finite systems. Section 4 discusses the legitimacy of applying TL to the problem of irreversibility and assesses the repercussions for its legitimacy on its home turf.

Type
Statistical Mechanics
Information
Philosophy of Science , Volume 68 , Issue S3: No. 3 Supplement: Proceedings of the 2000 Biennial Meeting of the Philosophy of Science Association. Part I: Contributed Papers Sep., 2001 , 2001 , pp. S325 - S344
Copyright
Copyright © Philosophy of Science Association 2001

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Footnotes

‡

I would like to thank Gérard Emch for discussions on topics I deal with in this paper. I would also like to thank Bob Batterman and Craig Callender for questions and comments on an earlier draft. This paper is supported in part by a NSF grant (SES-9910889).

References

Balashov, Yuri (1997), “Comments on R. Batterman's ‘Why Statistical Mechanics Works: Universality and the Renormalization Group‘”, preprint.Google Scholar
Batterman, Robert M. (1998), “Why Equilibrium Statistical Mechanics Works: Universality and the Renormalization Group”, Philosophy of Science 65:183–208.10.1086/392634CrossRefGoogle Scholar
Batterman, Robert M. (n.d.), “Multiple Realizability and Universality”, British Journal for Philosophy of Science, forthcoming.Google Scholar
Callender, Craig (1998), “The View from No-when”, British Journal for Philosophy of Science 49:135–159.CrossRefGoogle Scholar
Fisher, Michael E. (1982), “Scaling, Universality and Renormalization Group Theory”, in Hahne, F.J.W. (ed.), Critical Phenomena: Proceedings of the Summer School, The University of Stellenbosch, South Africa, January 18–29, 1982. Berlin: Springer-Verlag, 1–139.Google Scholar
Fisher, Michael E. (1998), “Renormalization Group Theory: Its Basis and Formulation in Statistical Physics”, Reviews of Modern Physics 70:653–681.10.1103/RevModPhys.70.653CrossRefGoogle Scholar
Fodor, Jerry (1974), “Special Sciences”, Synthese 28:77–115.Google Scholar
Goldenfeld, Nigel (1992), Lectures on Phase Transitions and the Renormalization Group. Reading, MA: Addison-Wesley.Google Scholar
Griffiths, Robert B. (1972), “Rigorous Results and Theorems”, in Domb, C. and Green, M. E. (eds.), Phase Transitions and Critical Phenomena. New York: Academic Press, 8–109.Google Scholar
Kac, Mark (1956), “Some Remarks on the Use of Probability in Classical Statistical Mechanics”, Bull Acad Roy Belg 42: 356.Google Scholar
Lanford III, Oscar E. (1983), “On the Derivation of the Boltzmann Equation”, in Lebowitz, J. L. and Montroll, E. W. (eds.), Nonequilibrium Phenomena I: The Boltzmann Equation. Amsterdam: North-Holland, 1–17.Google Scholar
Liu, Chuang (1999), “Explaining the Emergence of Cooperative Phenomena”, Philosophy of Science 66 (Supplement): s92–s106.10.1086/392718CrossRefGoogle Scholar
Nickles, Thomas (1973), “Two Concepts of Intertheoretic Reduction”, Journal of Philosophy 70:181–201.10.2307/2024906CrossRefGoogle Scholar
Onsager, Lars (1944), “Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition”, Physical Review 65:117–149.10.1103/PhysRev.65.117CrossRefGoogle Scholar
Schultz, T. D., Mattis, D. C., and Lieb, E. H. (1964), “Two-dimensional Ising Model as a Soluble Problem of Many Fermions”, Review of Modern Physics 36:856–871.10.1103/RevModPhys.36.856CrossRefGoogle Scholar
Sklar, Lawrence (1993), Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Stanley, H. Eugene (1971), Introduction to Phase Transitions and Critical Phenomena. Oxford: Clarendon Press.Google Scholar
Wannier, Gregory H. (1966), Statistical Physics. New York: Dover.Google Scholar
Wightman, Arthur S. (1979), “Introduction: Convexity and the Notion of Equilibrium State in Thermodynamics and Statistical Mechanics”, in Israel, R. B. (ed.), Convexity in the Theory of Lattice Gas. Princeton: Princeton University Press, ix–lxxxv.Google Scholar
Yang, C. N. (1972), “Introductory Note on Phase Transitions and Critical Phenomena”, in Domb, C. and Green, M. E. (eds.), Phase Transitions and Critical Phenomena. New York: Academic Press, 1–5.Google Scholar