References
Ainsworth, P. M. (2005). The spin-echo experiment and statistical mechanics. Foundations of Physics Letters, 18 (7), 621–35.
Albert, D. Z. (2000). Time and Chance. Cambridge, MA: Harvard University Press.
Albert, D. Z. (2015). After Physics. Cambridge, MA: Harvard University Press.
Anta, J. (2021). Ignorance, milk and coffee: can epistemic states be causally-explanatorily relevant in statistical mechanics? Foundations of Science, 28(2), 489–505.
Argyris, J., Faust, G., & Haase, M. (1994). An Exploration of Chaos: An Introduction for Natural Scientists and Engineers. Amsterdam: Elsevier.
Arnold, V. I., & Avez, A. (1968). Ergodic Problems of Classical Mechanics. New York and Amsterdam: W. A. Benjamin.
Badino, M. (2020). Reassessing typicality explanations in statistical mechanics. In Allori, V. (Ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature (pp. 147–72). Singapore: World Scientific.
Baras, D., & Shenker, O. (2020). Calling for explanation: the case of the thermodynamic past state. European Journal for Philosophy of Science, 10(3), 1–20.
Batterman, R. W. (2002). The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. Oxford: Oxford University Press.
Blatt, J. M. (1959). An alternative approach to the ergodic problem. Progress in Theoretical Physics, 22(6), 745–55.
Boltzmann, L. (1877). Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung resp. den Sätzen über das Wärmegleichgewicht. Wiener Berichte, 76, 373–435. Reprinted in F. Hasenöhrl (ed.), Wissenschaftliche Abhandlungen, Leipzig: J. A. Barth 1909, vol. 1902, pp. 1164–223.
Bricmont, J. (2001). Bayes, Boltzmann, and Bohm: probabilities in physics. In Bricmont, J., Ghirardi, G., & Dürr, D. et al. (Eds.), Chance in Physics Foundations and Perspectives (Lecture Notes in Physics). Berlin: Springer.
Bricmont, J. (2022). Making Sense of Statistical Mechanics. Cham: Springer.
Brown, H. R., & Uffink, J. (2001). The origin of time-asymmetry in thermodynamics: the minus first law. Studies in History and Philosophy of Modern Physics, 32(4), 525–38.
Brush, S. G. (1976). The Kind of Motion We Call Heat. Amsterdam: North Holland Publishing.
Butterfield, J. (2011a). Emergence, reduction and supervenience: a varied landscape. Foundations of Physics, 41(6), 920–59.
Butterfield, J. (2011b). Less is different: emergence and reduction reconciled. Foundations of Physics, 41(6), 1065–135.
Callender, C. (2004). There is no puzzle about the low-entropy past. In Hitchcock, C. (Ed.), Contemporary Debates in Philosophy of Science (pp. 240–55). Malden, MA: Blackwell.
Cartwright, N. (1999). The Dappled World: A Study of the Boundaries of Science. Cambridge: Cambridge University Press.
Cercignani, C. (1998). Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford: Oxford University Press.
Chandler, D. (1987). Introduction to Modern Statistical Mechanics. Oxford: Oxford University Press.
Chen, E. K. (2023). The past hypothesis and the nature of physical laws. In Loewer, B., Winsberg, E., & Weslake, B. (Eds.), Time’s Arrows and the Probability Structure of the World (pp. 204–248). Cambridge, MA: Harvard University Press.
Cornfeld, I. P., Fomin, S. V., & Sinai, Y. G. (1982). Ergodic Theory. Berlin: Springer.
Darrigol, O. (2018). Atoms, Mechanics, and Probability: Ludwig Boltzmann’s Statistico-Mechanical Writings – An Exegesis. Oxford: Oxford University Press.
Darrigol, O. (2021). Boltzmann’s reply to the Loschmidt paradox: a commented translation. The European Physical Journal H, 46(1), Article 29.
Davey, K. (2008). The justification of probability measures in statistical mechanics. Philosophy of Science, 75(1), 28–44.
Davey, K. (2009). What is Gibbs’s canonical distribution? Philosophy of Science, 76(5), 970–83.
Davies, P. (1974). The Physics of Time Asymmetry. Berkeley: University of California Press.
Dizadji-Bahmani, F. (2011). The Aharonov approach to equilibrium. Philosophy of Science, 78(5), 976–88.
Earman, J. (1986). A Primer on Determinism. Dordrecht: Reidel.
Earman, J. (2006). The past hypothesis: not even false. Studies in History and Philosophy of Modern Physics, 37(3), 399–430.
Earman, J., & Rédei, M. (1996). Why ergodic theory does not explain the success of equilibrium statistical mechanics. The British Journal for Philosophy of Science, 47(1), 63–78.
Ehrenfest, P., & Ehrenfest-Afanassjewa, T. (1912/1959). The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press.
Emch, G. G. (2007). Quantum statistical physics. In Butterfield, J. & Earman, J. (Eds.), Philosophy of Physics (pp. 1075–182). Amsterdam: North Holland.
Farquhar, I. E. (1964). Ergodic Theory in Statistical Mechanics. New York: Interscience Publishers.
Farr, M. (2022). What’s so special about initial conditions? Understanding the past hypothesis in directionless time. In Ben-Menahem, Y. (Ed.), Rethinking the Concept of Law of Nature: Natural Order in the Light of Contemporary Science (pp. 205–24). Cham: Springer.
Feynman, R. P. (1965). The Character of Physical Law. Cambridge, MA: Massachusetts Institute of Technology Press.
Fine, T. (1973). Theories of Probability: An Examination of Foundations. New York: Academic Press.
Frigg, R. (2008a). Chance in Boltzmannian statistical mechanics. Philosophy of Science, 75(5), 670–81.
Frigg, R. (2008b). A field guide to recent work on the foundations of statistical mechanics. In Rickles, D. (Ed.), The Ashgate Companion to Contemporary Philosophy of Physics (pp. 99–196). London: Ashgate.
Frigg, R. (2009). Typicality and the approach to equilibrium in Boltzmannian statistical mechanics. Philosophy of Science, 76(5), 997–1008.
Frigg, R. (2010). Probability in Boltzmannian statistical mechanics. In Ernst, G. & Hüttemann, A. (Eds.), Time, Chance and Reduction: Philosophical Aspects of Statistical Mechanics (pp. 92–118). Cambridge: Cambridge University Press.
Frigg, R. (2011). Why typicality does not explain the approach to equilibrium. In Suárez, M. (Ed.), Probabilities, Causes and Propensities in Physics (pp. 77–93, Synthese Library). Dordrecht: Springer.
Frigg, R. (2016). Chance and determinism. In Hájek, A. & Hitchcock, C. (Eds.), The Oxford Handbook of Probability and Philosophy (pp. 460–74). Oxford: Oxford University Press.
Frigg, R., & Hoefer, C. (2015). The best Humean system for statistical mechanics. Erkenntnis, 80(3), 551–74.
Frigg, R., & Werndl, C. (2011). Explaining thermodynamic-like behavior in terms of epsilon-ergodicity. Philosophy of Science, 78(3), 628–52.
Frigg, R., & Werndl, C. (2012). Demystifying typicality. Philosophy of Science, 79(5), 917–29.
Frigg, R., & Werndl, C. (2019). Statistical mechanics: a tale of two theories. The Monist, 102, 424–38.
Frigg, R., & Werndl, C. (2021). Can somebody please say what Gibbsian statistical mechanics says? The British Journal for Philosophy of Science, 72(1), 105–29.
Frigg, R., & Werndl, C. (2023). Boltzmannian non-equilibrium and local variables. In Soto, C. (Ed.), Current Debates in Philosophy of Science: In Honor of Roberto Torretti (pp. 275–287). Cham: Springer.
Frisch, M. (2011). From Arbuthnot to Boltzmann: the past hypothesis, the best system, and the special sciences. Philosophy of Science, 78(5), 1001–11.
Galavotti, M. C. (2005). Philosophical Introduction to Probability. Stanford, CA: CSLI Publications.
Gibbs, J. W. (1902/1981). Elementary Principles in Statistical Mechanics. Woodbridge: Oxbow Press.
Gillies, D. (2000). Philosophical Theories of Probability. London: Routledge.
Goldstein, S. (2001). Boltzmann’s approach to statistical mechanics. In Bricmont, J., Ghirardi, G., Dürr, D. et al. (Eds.), Chance in Physics. Foundations and Perspectives (pp. 39–54). Berlin: Springer.
Goldstein, S. (2019). Individualist and ensemblist approaches to the foundations of statistical mechanics. The Monist, 102, 439–57.
Goldstein, S., Lebowitz, J. L., Tumulka, R., & Zanghì, N. (2020). Gibbs and Boltzmann entropy in classical and quantum mechanics. In Allori, V. (Ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature (pp. 519–81). Singapore: World Scientific.
Hahn, E. L. (1950). Spin echoes. Physics Review, 80, 580–94.
Hand, D. J. (2008). Statistics: A Very Short Introduction. Oxford: Oxford University Press.
Hemmo, M., & Shenker, O. (2022). Is the Mentaculus the best system of our world? In Ben-Menahem, Y. (Ed.), Rethinking the Concept of Law of Nature: Natural Order in the Light of Contemporary Science (pp. 89–128). Cham: Springer.
Hill, T. L. (1956/1987). Statistical Mechanics: Principles and Selected Applications. Mineola, NY: Dover.
Hoefer, C. (2019). Chance in the World: A Humean Guide to Objective Chance (Oxford Studies in Philosophy of Science). New York: Oxford University Press.
Howson, C., & Urbach, P. (2006). Scientific Reasoning: The Bayesian Approach (3rd ed.). Chicago and La Salle: Open Court.
Isihara, A. (1971). Statistical Physics. London: Academic Press.
Jaynes, E. T. (1983). Papers on Probability, Statistics, and Statistical Physics. Dordrecht: Reidl.
Jebeile, J. (2020). The Kac ring or the art of making idealisations. Foundations of Physics, 50(10), 1152–70.
Katok, A., & Hasselblatt, B. (1995). Introduction to the Modern Theory of Dynamical Systems. Cambridge: Cambridge University Press.
Khinchin, A. I. (1949/1960). Mathematical Foundations of Statistical Mechanics. Mineola, NY: Dover Publications.
Kittel, C. (1958/2004). Elementary Statistical Physics. Mineola, NY: Dover Publications.
Landau, L. D., & Lifshitz, E. M. (1980). Statistical Physics: Part 1 (3rd ed.). Oxford: Pergamon.
Lavis, D. (2004). The spin-echo system reconsidered. Foundations of Physics, 34, 245–73.
Lavis, D. (2005). Boltzmann and Gibbs: An attempted reconciliation. Studies in History and Philosophy of Modern Physics, 36, 245–73.
Lavis, D., Kühn, R., & Frigg, R. (2021). Becoming large, becoming infinite. The anatomy of thermal physics and phase transitions in finite systems. Foundations of Physics, 51, 1–69.
Lavis, D., & Milligan, P. (1985). Essay review of Jaynes’ collected papers. The British Journal for Philosophy of Science, 36, 193–210.
Lavis, D. A. (2008). Boltzmann, Gibbs, and the concept of equilibrium. Philosophy of Science, 75, 682–96.
Lavis, D. A. (2015). Equilibrium Statistical Mechanics of Lattice Models. Cham: Springer.
Lebowitz, J. L. (1993). Macroscopic laws, microscopic dynamics, time’s arrow and Boltzmann’s entropy. Physica A, 194, 1–27.
Leeds, S. (1989). Malament and Zabell on Gibbs phase averaging. Philosophy of Science, 56, 325–40.
Lewis, D. K. (1986). A subjectivist’s guide to objective chance. In Philosophical Papers (pp. 83–132). Oxford: Oxford University Press.
Linden, N., Popesu, S., Short, A. J., & Andreas, W. (2009). Quantum mechanical evolution towards thermal equilibrium. Physical Review E, 79, Article 061103.
Loewer, B. (2001). Determinism and chance. Studies in History and Philosophy of Modern Physics, 32, 609–29.
Loschmidt, J. J. (1876). Über die Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft. Wiener Berichte, 73, 128–42.
Lyon, A. (2016). Kolmogorov’s axiomatisation and its discontents. In Hájek, A. & Hitchcock, C. (Eds.), The Oxford Handbook of Probability and Philosophy (pp. 155–66).
Malament, D. B., & Zabell, S. L. (1980). Why Gibbs phase averages work. Philosophy of Science, 47, 339–49.
Maudlin, T. (2020). The Grammar of Typicality. In Allori, V. (Ed.), Statistical Mechanics and Scientific Explanation. Determinism, Indeterminism and Laws of Nature (pp. 231–51). Singapore: World Scientific.
Maxwell, J. C. (1860/1965). Illustrations of the Dynamical Theory of Gases. In Niven, W. D. (Ed.), The Scientific Papers of James Clerk Maxwell (pp. 377–409). New York: Dover Publications.
McCoy, C. D. (2020). An Alternative Interpretation of Statistical Mechanics. Erkenntnis(85), 1–21.
Myrvold, W. C. (2016). Probabilities in statistical mechanics. In Hitchcock, C. & Hájek, A. (Eds.), Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press.
Myrvold, W. C. (2021). Beyond Chance and Credence: A Theory of Hybrid Probabilities. Oxford: Oxford University Press.
Palacios, P. (2022). Emergence and Reduction in Physics (Cambridge Elements). Cambridge: Cambridge University Press.
Parker, D. (2005). Thermodynamic irreversibility: does the big bang explain what it purports to explain? Philosophy of Science, 72(5), 751–63.
Pathria, R. K., & Beale, P. D. (2011). Statistical Mechanics (3rd ed.). Oxford: Academic Press.
Penrose, O. (1970). Foundations of Statistical Mechanics: A Deductive Treatment (Oxford). Pergamon Press.
Penrose, R. (2006). The Road to Reality: A Complete Guide to the Laws of the Universe. London: Vintage.
Petersen, K. (1983). Ergodic Theory. Cambridge: Cambridge University Press.
Price, H. (2004). On the origins of the arrow of time: why there is still a puzzle about the low-entropy past. In Hitchcock, C. (Ed.), Contemporary Debates in Philosophy of Science (pp. 219–39). Malden, MA: Blackwell.
Rédei, M. (1992). Krylov’s proof that statistical mechanics cannot be founded on classical mechanics and interpretation of classical statistical mechanical probabilities. Philosophia Naturalis, 29, 268–84.
Redhead, M. L. G. (1995). From Physics to Metaphysics. Cambridge: Cambridge University Press.
Reiss, H. (1965). Methods of Thermodynamics. New York: Blaisdell Publishing Company.
Ridderbos, K. (2002). The coarse-graining approach to statistical mechanics: How blissful is our ignorance? Studies in History and Philosophy of Modern Physics, 33, 65–77.
Ridderbos, T. M., & Redhead, M. L. G. (1998). The spin-echo experiments and the second law of thermodynamics. Foundations of Physics, 28, 1237–70.
Roberts, B. W. (2022). Reversing the Arrow of Time. Cambridge: Cambridge University Press.
Robertson, K. (2020). Asymmetry, abstraction and autonomy: justifying coarse-graining in statistical mechanics. The British Journal for the Philosophy of Science, 71(2), 547–79.
Schrödinger, E. (1952/1989). Statistical Thermodynamics. Mineola, NY: Dover.
Shenker, O. (2017a). Foundation of statistical mechanics: mechanics by itself. Philosophy Compass, 12(12), e12465.
Shenker, O. (2017b). Foundation of statistical mechanics: the auxiliary hypotheses. Philosophy Compass, 12(12), e12464.
Shenker, O. (2020). Information vs. entropy vs. probability. European Journal for Philosophy of Science, 10, Article No 5.
Sklar, L. (1993). Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge: Cambridge University Press.
te Vrug, M., Tóth, G. I., & Wittkowski, R. (2021). Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility. Journal of Computational Electronics, 20, 2209–31.
Tolman, R. C. (1938/1979). The Principles of Statistical Mechanics. Mineola, NY: Dover.
Uffink, J. (1995). Can the maximum entropy principle be explained as a consistency requirement? Studies in History and Philosophy of Modern Physics, 26, 223–61.
Uffink, J. (1996a). The constraint rule of the maximum entropy principle. Studies in History and Philosophy of Modern Physics, 27, 47–79.
Uffink, J. (1996b). Nought but molecules in motion (review essay of Lawrence Sklar: Physics and Chance). Studies in History and Philosophy of Modern Physics, 27, 373–87.
Uffink, J. (2001). Bluff your way in the second law of thermodynamics. Studies in History and Philosophy of Modern Physics, 32, 305–94.
Uffink, J. (2007). Compendium of the foundations of classical statistical physics. In Butterfield, J. & Earman, J. (Eds.), Philosophy of Physics (pp. 923–1047).
Uffink, J. (2011). Subjective probability and statistical physics. In Beisbart, C. & Hartmann, S. (Eds.), Probabilities in Physics (pp. 25–49). Oxford: Oxford University Press.
van Lith, J. (2001). Ergodic theory, interpretations of probability and the foundations of statistical mechanics. Studies in History and Philosophy of Modern Physics, 32, 581–94.
von Plato, J. (1988). Ergodic theory and the foundations of probability. In Skyrms, B. & Harper, W. W. (Eds.), Causation, Chance and Credence (pp. 257–77). Dordrecht: Kluwer.
von Plato, J. (1989). Probability in dynamical systems. In Fenstad, J. E., Frolov, I. T., & Hilpinen, R. (Eds.), Logic, Methodology and Philosophy of Science, Vol. VIII (pp. 427–43). Amsterdam: North-Holland.
Vranas, P. B. M. (1998). Epsilon-ergodicity and the success of equilibrium statistical mechanics. Philosophy of Science, 65, 688–708.
Wallace, D. (2015). The quantitative content of statistical mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, 285–93.
Wallace, D. (2020). The necessity of Gibbsian statistical mechanics. In Allori, V. (Ed.), Statistical Mechanics and Scientific Explanation. Determinism, Indeterminism and Laws of Nature (pp. 583–616). World Scientific.
Wells, J. D. (2012). Effective Theories in Physics: From Planetary Orbits to Elementary Particle Masses. Heidelberg: Springer.
Werndl, C. (2013). Justifying typicality measures of Boltzmannian statistical mechanics and dynamical systems. Studies in History and Philosophy of Modern Physics, 44(4), 470–9.
Werndl, C., & Frigg, R. (2015a). Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence. Studies in History and Philosophy of Modern Physics, 49(1), 19–31.
Werndl, C., & Frigg, R. (2015b). Rethinking Boltzmannian equilibrium. Philosophy of Science, 82(5), 1224–35.
Werndl, C., & Frigg, R. (2017a). Boltzmannian equilibrium in stochastic systems. In Massimi, M. & Romeijn, J.-W. (Eds.), Proceedings of the EPSA15 Conference (pp. 243–54). Berlin: Springer.
Werndl, C., & Frigg, R. (2017b). Mind the gap: Boltzmannian vs Gibbsian equilibrium. Philosophy of Science, 84, 1289–1302.
Werndl, C., & Frigg, R. (2020a). Taming abundance: on the relation between Boltzmannian and Gibbsian statistical mechanics. In Allori, V. (Ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature (pp. 617–46). World Scientific.
Werndl, C., & Frigg, R. (2020b). When do Gibbsian phase averages and Boltzmannian equilibrium values agree? Studies in History and Philosophy of Modern Physics, 72, 46–69.
Werndl, C., & Frigg, R. (2023). When does a Boltzmannian equilibrium exist? In Soto, C. (Ed.), Current Debates in Philosophy of Science: In Honor of Roberto Torretti (pp. forthcoming). Cham: Springer.
Wilhelm, I. (2022). Typical: a theory of typicality and typicality explanation. The British Journal for the Philosophy of Science, 73(2), 561–81.
Williamson, J. (2010). In Defence of Objective Bayesianism. Oxford: Oxford University Press.
Winsberg, E. (2004a). Can conditioning on the ‘past hypothesis’ militate against the reversibility objection? Philosophy of Science, 71, 489–504.
Winsberg, E. (2004b). Laws and statistical mechanics. Philosophy of Science, 71, 707–18.
Zanghì, N. (2005). I Fondamenti concettuali dell’approccio statistico in Fisica. In Allori, V., Dorato, M., Laudisa, F., & Zanghì, N. (Eds.), La Natura Delle Cose: Introduzione ai Fundamenti e alla Filosofia della Fisica (pp. 139–227). Roma: Carocci.
Zermelo, E. (1896). Über einen Satz der Dynamik und die mechanische Wärmetheorie. Annalen der Physik, 57, 485–94.
