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A Justification of the Probabilistic Explanation of the Entropy Principle
Published online by Cambridge University Press: 01 January 2022
Abstract
In many ways, entropy and probability are two concepts that complement each other. But it has been argued that there is no ‘straightforward connection’ between them with a no-go thesis from Kevin Davey. However, this skeptical conclusion rests on counterexamples that fail to do justice to the entropy principle and the equivocality of the notion of probability. Proceeding from the disambiguation of probability, and acknowledging the explanatory goal of the entropy principle, it is argued that the Boltzmannian statistical mechanics account can be vindicated with a justification of the explanandum, the reference class, and the standard uniform probability measure.
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References
Batterman, Robert W. 2002. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. Oxford: Oxford University Press.Google Scholar
Brown, Harvey R., Myrvold, Wayne, and Uffink, Jos. 2009. “Boltzmann’s H-Theorem, Its Discontents, and the Birth of Statistical Mechanics.” Studies in History and Philosophy of Modern Physic 40:174–91.Google Scholar
Callender, Craig. 1999. “Reducing Thermodynamics to Statistical Mechanics: The Case of Entropy.” Journal of Philosophy 96:348–73.Google Scholar
Capek, Vladislav, and Sheehan, Daniel P.. 2005. Challenges to the Second Law of Thermodynamics: Theory and Experiment. Dordrecht: Springer.CrossRefGoogle Scholar
Carnap, Rudolf. 1977. Two Essays on Entropy. Berkeley: University of California Press.CrossRefGoogle Scholar
Castell, Paul. 1998. “A Consistent Restriction of the Principle of Indifference.” British Journal of Philosophy of Science 49:387–95.CrossRefGoogle Scholar
Clausius, R. J. E. 1854. “On Another Form of the Second Principle of the Mechanical Theory of Heat.” Annalen der Physik und Chemie 93:481–506, trans. Philosophical Magazine, ser. 4, 12, no. 81 (1856).CrossRefGoogle Scholar
Davey, Kevin. 2008. “The Justification of Probability Measures in Statistical Mechanics.” Philosophy of Science 75:28–44.CrossRefGoogle Scholar
Davey, Kevin. 2011. “Thermodynamic Entropy and Its Relation to Probability in Classical Mechanics.” Philosophy of Science 78:955–75.CrossRefGoogle Scholar
Denbigh, Kenneth G. 1989. “Note on Entropy, Disorder and Disorganization.” British Journal for the Philosophy of Science 40:323–32.CrossRefGoogle Scholar
Frigg, Roman. 2010a. “Probability in Boltzmannian Statistical Mechanics.” In Time, Chance and Reduction, ed. Ernst, G. and Hütteman, A., 92–118. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Frigg, Roman. 2010b. “Why Typicality Does Not Explain the Approach to Equilibrium.” In Probabilities, Causes and Propensities in Physics, ed Suàrez, Mauricio, 77–93. Dordrecht: Springer.Google Scholar
Frigg, Roman, and Werndl, Charlotte. 2011. “Entropy: A Guide for the Perplexed.” In Probability in Physics, ed. Beisbart, C. and Hartmann, S., 115–42. Oxford: Oxford University Press.Google Scholar
Goldstein, Sheldon. 2001. “Boltzmann’s Approach to Statistical Mechanics.” In Chance in Physics: Foundations and Perspectives, ed. Bricmont, J., et al., 39–54. Lecture Notes in Physics 574. Berlin: Springer.CrossRefGoogle Scholar
Goldstein, Sheldon, and Lebowitz, Joel L.. 2004. “On the (Boltzmann) Entropy of Nonequilibrium Systems.” Physica D 193:53–66.Google Scholar
Hájek, Alan, and Hall, Ned. 2002. “Induction and Probability.” In The Blackwell Guide to the Philosophy of Science, ed. Machamer, P. and Silberstein, M., 149–72. Oxford: Blackwell.Google Scholar
Handfield, Toby. 2012. A Philosophical Guide to Chance. New York: Cambridge University Press.CrossRefGoogle Scholar
Ismael, Jenann T. 2009. “Probability in Deterministic Physics.” Journal of Philosophy 106:89–108.CrossRefGoogle Scholar
Khinchin, Aleksandr I. 1949. Mathematical Foundations of Statistical Mechanics. New York: Dover.Google Scholar
Landau, Lev D., and Lifshitz, Evgueni M.. 1980. Statistical Physics. 3rd ed. New York: Pergamon.Google Scholar
Leeds, S. 2003. “Foundations of Statistical Mechanics: Two Approaches.” Philosophy of Science 70:126–44.CrossRefGoogle Scholar
Lieb, Elliott H., and Yngvason, Jakob. 2003. “The Mathematical Structure of the Second Law of Thermodynamics.” arXiv, Cornell University. https://arxiv.org/abs/math-ph/0204007.Google Scholar
Penrose, Oliver. 1979. “Foundations of Statistical Mechanics.” Reports on Progress in Physics 42:1939–97.CrossRefGoogle Scholar
Railton, Peter. 1981. “Probability, Explanation, and Information.” Synthese 48:233–56.CrossRefGoogle Scholar
Shech, Elay. 2013. “On Gases in Boxes: A Reply to Davey on the Justification of the Probability Measure in Boltzmannian Statistical Mechanics.” Philosophy of Science 80:593–605.CrossRefGoogle Scholar
Sklar, Lawrence. 1973. “Statistical Explanation and Ergodic Theory.” Philosophy of Science 40:194–212.CrossRefGoogle Scholar
Sklar, Lawrence. 1993. Physics and Chance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Strevens, Michael. 2014. “Probabilistic Explanation.” In Physical Theory: Method and Interpretation, ed. Sklar, L., 40–62. Oxford: Oxford University Press.CrossRefGoogle Scholar
Uffink, Jos. 2007. “Compendium of the Foundations of Classical Statistical Physics.” In Philosophy of Physics, pt. B, ed. Butterfield, J. and Earman, J., 923–1074. Amsterdam: Elsevier.CrossRefGoogle Scholar
Werndl, Charlotte. 2013. “Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems.” Studies in History and Philosophy of Modern Physic 44:470–79.Google Scholar