Hostname: page-component-857557d7f7-zntvd Total loading time: 0 Render date: 2025-11-21T22:13:41.598Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase Transitions: A Challenge for Intertheoretic Reduction?

Published online by Cambridge University Press:  01 January 2022

Patricia Palacios
Get access Rights & Permissions [Opens in a new window]

Abstract

I analyze the extent to which classical phase transitions, both first order and continuous, pose a challenge for intertheoretic reduction. My contention is that phase transitions are compatible with a notion of reduction that combines Nagelian reduction and what Thomas Nickles called Reduction2. I also argue that, even if the same approach to reduction applies to both types of phase transitions, there is a crucial difference in their physical treatment: in addition to the thermodynamic limit, in continuous phase transitions there is a second infinite limit involved, which marks an important difference in the reduction of first-order and continuous phase transitions.

Information

Type
Research Article
Information
Philosophy of Science , Volume 86 , Issue 4 , October 2019 , pp. 612 - 640
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

†

I am extremely grateful to Vincent Ardourel, Federico Benitez, Lapo Casetti, Erik Curiel, Benjamin Feintzeig, Sam Fletcher, Roman Frigg, Stephan Hartmann, Laurenz Hudetz, Karim Thébault, Giovanni Valente, Pauline van Wierst, Jim Weatherall, Charlotte Werndl and Jingyi Wu for helpful discussions and detailed comments on an earlier draft. I am also grateful to two anonymous referees for their helpful comments.

References

Ardourel, V. 2018. “The Infinite Limit as an Eliminable Approximation for Phase Transitions.” Studies in History and Philosophy of Science B 62:71–84.CrossRefGoogle Scholar
Bangu, S. 2009. “Understanding Thermodynamic Singularities: Phase Transitions, Data, and Phenomena.” Philosophy of Science 76 (4): 488–505..CrossRefGoogle Scholar
Bangu, S.. 2011. “On the Role of Bridge Laws in Intertheoretic Relations.” Philosophy of Science 78 (5): 1108–19..CrossRefGoogle Scholar
Batterman, R. W. 2001. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. Oxford: Oxford University Press.CrossRefGoogle Scholar
Batterman, R. W.. 2005. “Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics.” Studies in History and Philosophy of Science B 36 (2): 225–44..Google Scholar
Batterman, R. W.. 2011. “Emergence, Singularities and Symmetry Breaking.” Foundations of Physics 41 (6): 1031–50..CrossRefGoogle Scholar
Batterman, R. W.. 2017. “Philosophical Implications of Kadanoff’s Work on the Renormalization Group.” Journal of Statistical Physics 167 (3–4): 559–74.CrossRefGoogle Scholar
Batterman, R. W., and Rice, C.. 2014. “Minimal Model Explanations.” Philosophy of Science 81 (3): 349–76..CrossRefGoogle Scholar
Borrmann, P., Mülken, O., and Harting, J.. 2000. “Classification of Phase Transitions in Small Systems.” Physical Review Letters 84 (16): 3511.CrossRefGoogle ScholarPubMed
Butterfield, J. 2011. “Less Is Different: Emergence and Reduction Reconciled.” Foundations of Physics 41 (6): 1065–35..CrossRefGoogle Scholar
Butterfield, J., and Bouatta, N.. 2012. “Emergence and Reduction Combined in Phase Transitions.” In Frontiers of Fundamental Physics: The Eleventh International Symposium, ed. Kouneiher, Joseph, 383–403. AIP Conference Proceedings 1446. Melville, NY: American Institute of Physics.Google Scholar
Callender, C. 2001. “Taking Thermodynamics Too Seriously.” Studies in History and Philosophy of Science B 32 (4): 539–53..Google Scholar
Casetti, L., and Kastner, M.. 2006. “Nonanalyticities of Entropy Functions of Finite and Infinite Systems.” Physical Review Letters 97 (10): 100602.CrossRefGoogle ScholarPubMed
Dizadji-Bahmani, F., Frigg, R., and Hartmann, S.. 2010. “Who’s Afraid of Nagelian Reduction?” Erkenntnis 73 (3): 393–412..CrossRefGoogle Scholar
Domb, C. 2000. Phase Transitions and Critical Phenomena. vol. 19. London: Elsevier.Google Scholar
Fisher, M. E. 1998. “Renormalization Group Theory: Its Basis and Formulation in Statistical Physics.” Reviews of Modern Physics 70 (2): 653–81..CrossRefGoogle Scholar
Fisher, M. E., and Berker, A. N.. 1982. “Scaling for First-Order Phase Transitions in Thermodynamic and Finite Systems.” Physical Review B 26 (5): 2507–13..Google Scholar
Franklin, A. 2017. “On the Renormalisation Group Explanation of Universality.” Philosophy of Science 85 (2): 225–48..Google Scholar
Goldenfeld, N. 1992. Lectures on Phase Transitions and the Renormalization Group. Boulder, CO: Westview.Google Scholar
Gross, D. H. 2001. Microcanonical Thermodynamics: Phase Transitions in “Small” Systems. Singapore: World Scientific.CrossRefGoogle Scholar
Haller, K., and Kennedy, T.. 1996. “Absence of Renormalization Group Pathologies Near the Critical Temperature.” Journal of Statistical Physics 85 (5): 607–37..CrossRefGoogle Scholar
Kadanoff, L. P. 2009. “More Is the Same: Phase Transitions and Mean Field Theories.” Journal of Statistical Physics 137 (5–6): 777–97.CrossRefGoogle Scholar
Kaplan, D. 2011. “Explanation and Description in Computational Neuroscience.” Synthese 183 (3): 339–73..CrossRefGoogle Scholar
Landsman, N. P. 2013. “Spontaneous Symmetry Breaking in Quantum Systems: Emergence or Reduction?” Studies in History and Philosophy of Science B 44 (4): 379–94..Google Scholar
Le Bellac, M., Mortessagne, F., and Batrouni, G.. 2006. Equilibrium and Non-equilibrium Statistical Thermodynamics. Cambridge: Cambridge University Press.Google Scholar
Ma, S.-K. 1976. “Renormalization Group by Monte Carlo Methods.” Physical Review Letters 37 (8): 461–64..CrossRefGoogle Scholar
Mainwood, P. 2006. “Phase Transitions in Finite Systems.” PhD diss., University of Oxford.Google Scholar
Menon, T., and Callender, C.. 2013. “Ch-ch-changes Philosophical Questions Raised by Phase Transitions.” In The Oxford Handbook of Philosophy of Physics, ed. Batterman, R., 189–223. Oxford: Oxford University Press.Google Scholar
Morrison, M. 2012. “Emergent Physics and Micro-Ontology.” Philosophy of Science 79 (1): 141–66..CrossRefGoogle Scholar
Nagel, E. 1970. “Issues in the Logic of Reductive Explanations.” In Mind, Science and History, ed. Munitz, H. K., 117–37. Albany, NY: SUNY Press.Google Scholar
Nickles, T. 1973. “Two Concepts of Intertheoretic Reduction.” Journal of Philosophy 70 (7): 181–201..CrossRefGoogle Scholar
Norton, J. D. 2012. “Approximation and Idealizations: Why the Difference Matters.” Philosophy of Science 79 (2): 207–32..CrossRefGoogle Scholar
Norton, J. D.. 2013. “Confusions over Reduction and Emergence in the Physics of Phase Transitions.” Unpublished manuscript. http://www.pitt.edu/-jdnorton/Goodies/reductionemergence/redem.html.Google Scholar
Palacios, P. 2018. “Had We but World Enough, and Time … but We Don’t! Justifying the Thermodynamic and Infinite-Time Limits in Statistical Mechanics.” Foundations of Physics 5 (48): 526–41..Google Scholar
Pawley, G., Swendsen, D., Wallace, R. H., and Wilson, K. G.. 1984. “Monte Carlo Renormalization-Group Calculations of Critical Behavior in the Simple-Cubic Ising Model.” Physical Review 29 (7): 4030–40..Google Scholar
Rosaler, J. 2017. “Reduction as an a Posteriori Relation.” British Journal for the Philosophy of Science 70 (1): 269–99..Google Scholar
Rueger, A. 2000. “Physical Emergence, Diachronic and Synchronic.” Synthese 124 (3): 297–322..CrossRefGoogle Scholar
Schaffner, K. F. 1967. “Approaches to Reduction.” Philosophy of Science 34 (2): 137–47..CrossRefGoogle Scholar
Schmelzer, J., and Ulbricht, H.. 1987. “Thermodynamics of Finite Systems and the Kinetics of First-Order Phase Transitions.” Journal of Colloid and Interface Science 117 (2): 325–38..CrossRefGoogle Scholar
Sornette, D. 2000. Critical Phenomena in Natural Sciences. Dordrecht: Springer.CrossRefGoogle Scholar
Wilson, K., and Kogut, J.. 1974. “The Renormalization Group and the ε Expansion.” Physics Reports 12 (2): 75–199..CrossRefGoogle Scholar
Yin, M. 2011. “Renormalization Group Transformations Near the Critical Point: Some Rigorous Results.” Journal of Mathematical Physics 52 (11): 113507.CrossRefGoogle Scholar