Explaining irreversibility

American Journal of Physics

Volumn 76, Issue 7, 2008, Pages 643-648

  Swendsen, Robert H ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48249144417     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2894523     Document Type: Article

References (15)

1. P. Coveney and R. Highfield, The Arrow of Time (W. H. Allan, London, 1990). This book contains a good discussion of the debate about irreversibility.
2. H. L. Frisch, "An approach to equilibrium," Phys. Rev. 109, 22-29 (1958).
3. A. Georgallas, "Free expansion of an ideal gas into a box: An exactly solvable approach to equilibrium," Phys. Rev. A 35, 3492-3498 (1987).
4. L. Boltzmann, "Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen," Wien. Ber. 66, 275-370 (1872). The German word "Stoss" refers to a collision, "Zahl" means number, and "Ansatz" has become an English word for the starting point, or initial approximation.
5. J. Loschmidt, "Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft," Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt. 2A 73, 128-142 (1876).
6. E. Zermelo, "Über einen Satz der Dynamik und die mechanische Wärmelehre," Ann. Phys. 57, 485-494 (1896).
7. E. Zermelo, "Über mechanische Erklärungen irreversibler Vorgänge. Eine Antwort auf Hrn. Boltzmann's 'Entgegnung'," Ann. Phys. 59, 793-801 (1896).
8. M. Planck, "Über das Gesetz der Energieverteilung im Normalspectrum," Ann. Phys. 309, 553-563 (1901).
9. "Umkehr" means "reversal," referring to the reversal of velocities in Loschmidt's argument. "Einwand" means "objection."
10. H. Poincaré, "Sur le probleme des trois corps et les équations de la dynamique," Acta Math. 13, 1-270 (1890).
11. "Wiederkehr" means "return" or "recur," referring to the return to the original state in Zermelo's argument.
12. If the period of each molecule divided into the longest period is an integer, the recurrence time will be equal to the longest period. It will not be astronomically long. Therefore, a probabilistic argument is necessary to establish that the recurrence time is extraordinarily long.
13. E. L. Hahn, "Spin echos," Phys. Rev. 80, 580-594 (1950).
14. R. K. Pathria, Statistical Mechanics (Pergamon, New York, 1972). pp. 34-36.
15. R. H. Swendsen, "Statistical mechanics of colloids and Boltzmann's definition of the entropy," Am. J. Phys. 74, 187-190 (2006).