Dynamics of a massive piston in an ideal gas

Russian Mathematical Surveys

Volumn 57, Issue 6, 2002, Pages 1045-1125

  Chernov, N I ^a   Lebowitz, J L ^a   Sinai, Ya G ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037651092     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2002v057n06ABEH000572     Document Type: Review

References (27)

1. L. Boltzmann, "Reply to Zermelo's remarks on the theory of heat", Ann. Phys. 57 (1896), 773, reprinted and translated as Chap. 8 in S. G. Brush, Kinetic Theory, Pergamon, Oxford 1996.
2. B. Cagliotti, N. Chernov, and J. L. Lebowitz, "Stability of solutions of hydrodynamic equations describing the scaling limit of a massive piston in an ideal gas", www.math.uab.edu/chernov/papers/pubs.html.
3. H. B. Callen, Thermodynamics, Wiley, New York 1963, Appendix C.
4. N. Chernov and J. L. Lebowitz, "Dynamics of a massive piston in an ideal gas: Oscillatory motion and approach to equilibrium", J. Statist. Phys. 109 (2002), 507-527.
5. N. Chernov, "Entropy, Lyapunov exponents, and mean-free path for billiards", J. Statist. Phys. 88 (1997), 1-29.
6. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic theory, Nauka, Moscow 1980; English transl., Springer-Verlag, New York 1982.
7. B. Crosignani, P. Di Porto, and M. Segev, "Approach to thermal equilibrium in a system with adiabatic constraints", Amer. J. Phys. 64 (1996), 610-613.
8. D. Dürr, S. Goldstein, and J. L. Lebowitz, "A mechanical model of Brownian motion", Comm. Math. Phys. 78 (1981), 507-530.
9. R. Feynman, R. Leighton, and M. Sands, The Feynman lectures in physics, I, Commemorative Issue, Addison-Wesley, Redwood City, CA 1989, Chap. 39.
10. C. Gruber, "Thermodynamics of systems with internal adiabatic constraints: time evolution of the adiabatic piston", European J. Phys. 20 (1999), 259-266.
11. C. Gruber and L. Frachebourg, "On the adiabatic properties of a stochastic adiabatic wall: Evolution, stationary non-equilibrium, and equilibrium states", Phys. A 272 (1999), 392-428.
12. C. Gruber and J. Piasecki, "Stationary motion of the adiabatic piston", Phys. A 268 (1999), 412-423.
13. R. Holley, "The motion of a heavy particle in an infinite one-dimensional gas of hard spheres", Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 17 (1971), 181-219.
14. S. Kerckhoff, H. Masur, and J. Smillie, "Ergodicity of billiard flows and quadratic differentials", Ann. of Math. (2) 124 (1986), 293-311.
15. E. Kestemont, C. van den Broeck, and M. Mansour, "The 'adiabatic' piston: and yet it moves", Europhys. Lett. 49 (2000), 143-149.
16. A. N. Kolmogorov and V. M. Tihomirov, "ε-entropy and ε-capacity of sets in function spaces", Uspekhi Mat. Nauk 14:2 (1959), 3-86; English transl., Amer. Math. Soc. Transl. (2) 17 (1961), 277-364.
17. A. N. Kolmogorov and V. M. Tihomirov, "ε-entropy and ε-capacity of sets in function spaces", Uspekhi Mat. Nauk 14:2 (1959), 3-86; English transl., Amer. Math. Soc. Transl. (2) 17 (1961), 277-364.
18. R. Kubo, Statistical mechanics, North-Holland, Amsterdam 1965, see pp. 11-17.
19. L. D. Landau and E. M. Lifshitz, Statistical mechanics, Nauka, Moscow 1976; English transl., Pergamon, Oxford 1980, see pp. 32-41.
20. J. L. Lebowitz, J. Piasecki, and Ya. Sinai, "Scaling dynamics of a massive piston in an ideal gas", Hard Ball Systems and Lorentz Gas (Encyclopaedia Math. Sci., vol. 101), Springer-Verlag, Berlin, 2000, pp. 217-227.
21. J. L. Lebowitz, "Stationary non-equilibrium Gibbsian ensembles", Phys. Rev. (2) 114 (1959), 1192-1202.
22. E. Lieb, "Some problems in statistical mechanics that I would like to see solved", Phys. A 263 (1999), 491-499.
23. R. Lupton, Statistics in theory and practice, Princeton Univ. Press, Princeton, NJ 1993.
24. M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator", ACM Trans. Model. Comput. Simul. 8 (1998), 3-30.
25. E. Nelson, Dynamical theories of Brownian motion, Princeton Univ. Press, Princeton, NJ 1967.
26. J. Piasecki and C. Gruber, "From the adiabatic piston to macroscopic motion induced by fluctuation", Phys. A 265 (1999), 463-472.
27. A. N. Tikhonov, A. B. Vasil'eva, and A. G. Sveshnikov, Differential equations, Nauka, Moscow 1985; English transl., Springer-Verlag, Berlin 1985.