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On How to Approach the Approach to Equilibrium

Published online by Cambridge University Press:  01 January 2022

Abstract

This article highlights the limitations of typicality accounts of thermodynamic behavior so as to promote an alternative line of research: understanding and accounting for the success of the techniques and equations physicists use to model the behavior of systems that begin away from equilibrium. This article also takes steps in this promising direction. It examines a technique commonly used to model the behavior of an important kind of system: a Brownian particle that has been introduced to an isolated fluid at equilibrium. It also accounts for the success of the model, by identifying and grounding the technique’s key assumptions.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

Very special thanks to Wayne Myrvold for helpful discussions and comments on earlier drafts. Special thanks to Carl Hoefer, Markus Müller, Chris Smeenk, and David Wallace for helpful discussions and comments on work related to this project. Thanks to Jeremy Butterfield, Jos Uffink, and other audience members at CLMPS for helpful comments on a presentation of this work. Thanks also to two anonymous referees for helpful comments.

References

Berkovitz, Joseph, Frigg, Roman, and Kronz, Fred. 2006. “The Ergodic Hierarchy, Randomness and Hamiltonian Chaos.” Studies in History and Philosophy of Science B 37 (4): 661–91.Google Scholar
Boltzmann, Ludwig. 1877. “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung resp. den Sätzen über das Wärmegleichgewicht.” Wiener Berichte 76:373435.Google Scholar
de Grooth, Bart G. 1999. “A Simple Model for Brownian Motion Leading to the Langevin Equation.” American Journal of Physics 67 (12): 1248–52.CrossRefGoogle Scholar
Ehrenfest, P., and Ehrenfest, T.. 2002. The Conceptual Foundations of the Statistical Approach in Mechanics. New York: Dover.Google Scholar
Frigg, Roman. 2009. “Typicality and the Approach to Equilibrium in Boltzmannian Statistical Mechanics.” Philosophy of Science 76 (5): 9971008.CrossRefGoogle Scholar
Frigg, Roman 2011. “Why Typicality Does Not Explain the Approach to Equilibrium.” In Probabilities, Causes and Propensities in Physics, Vol. 347, ed. M. Suárez, 77–93. Dordrecht: Springer.CrossRefGoogle Scholar
Frigg, Roman, Berkovitz, Joseph, and Kronz, Fred. 2014. “The Ergodic Hierarchy.” In The Stanford Encyclopedia of Philosophy, ed. Zalta, Edward N.. Stanford, CA: Stanford University.Google Scholar
Goldstein, S. 2001. “Boltzmann’s Approach to Statistical Mechanics.” In Chance in Physics, ed. Bricmont, J., Ghirardi, G., Dürr, D., Petruccione, F., Galavotti, M.-C., and Zanghì, N., 3954. Lecture Notes in Physics 574. Berlin: Springer.CrossRefGoogle Scholar
Goldstein, S., and Lebowitz, J. L.. 2004. “On the (Boltzmann) Entropy of Non-equilibrium Systems.” Physica D: Nonlinear Phenomena 193:5366.CrossRefGoogle Scholar
Kadanoff, Leo. 2000. Statistical Physics: Statics, Dynamics and Renormalization. River Edge, NJ: World Scientific.CrossRefGoogle Scholar
Lanford, O. E. III. 1975. “Time Evolution of Large Classical Systems.” In Dynamical Systems, Theory and Applications, ed. Moser, J., 1111. Lecture Notes in Physics 38. Berlin: Springer.Google Scholar
Moser, J. 1976. “On a Derivation of the Boltzmann Equation.” In Nonequilibrium Phenomena I: The Boltzmann Equation, ed. Lebowitz, J. L. and Montroll, E. W., 117. Studies in Statistical Mechanics 10. Amsterdam: North-Holland.Google Scholar
Montroll, E. W. 1981. “The Hard Sphere Gas in the Boltzmann-Grad Limit.” Physica A: Statistical Mechanics and Its Applications 106:7076.Google Scholar
Lebowitz, J. L. 1993a. “Boltzmann’s Entropy and Time’s Arrow.” Physics Today 46:3238.CrossRefGoogle Scholar
Lebowitz, J. L. 1993b. “Macroscopic Laws, Microscopic Dynamics, Time’s Arrow and Boltzmann’s Entropy.” Physica A: Statistical Mechanics and Its Applications 194:127.CrossRefGoogle Scholar
Lebowitz, J. L. 1999. “Statistical Mechanics: A Selective Review of Two Central Issues.” Reviews of Modern Physics 71 (2): 346–57.CrossRefGoogle Scholar
Mazenko, Gene. 2006. Nonequilibrium Statistical Mechanics. London: Wiley.CrossRefGoogle Scholar
Pathria, Raj, and Beale, Paul. 2011. Statistical Mechanics. 3rd ed. New York: Academic Press.Google Scholar
Price, Huw. 1996. Time’s Arrow and Archimedes’ Point. Oxford: Oxford University Press.Google Scholar
Reif, Frederick. 1965. Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hill.Google Scholar
Uffink, Jos. 2007. “Compendium of the Foundations of Classical Statistical Physics.” In Philosophy of Physics, ed. Butterfield, J. and Earman, J.. Amsterdam: North-Holland.Google Scholar
Uffink, Jos, and Valente, Giovanni. 2015. “Lanford’s Theorem and the Emergence of Irreversibility.” Foundations of Physics 45 (4): 404–38.CrossRefGoogle Scholar
Valente, Giovanni. 2014. “The Approach towards Equilibrium in Lanford’s Theorem.” European Journal for Philosophy of Science 4:309–35.CrossRefGoogle Scholar
Werndl, Charlotte. 2013. “Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems.” Studies in History and Philosophy of Science B 44 (4): 470–79.Google Scholar
Werndl, Charlotte, and Frigg, Roman. 2015. “Reconceptualising Equilibrium in Boltzmannian Statistical Mechanics and Characterising Its Existence.” Studies in History and Philosophy of Science B 49:1931.CrossRefGoogle Scholar
Zwanzig, Robert. 2001. Nonequilibrium Statistical Mechanics. Oxford: Oxford University Press.Google Scholar