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An invertibility paradox
1.Maxwell’s Demon: Entropy, Information, Computing, edited by H. S. Leff and A. F. Rex (Princeton U.P., Princeton, 1990).
2.See, for example, S. G. Brush, The Kind of Motion We Call Heat (North-Holland, Amsterdam, 1986).
3.L. Boltzmann, Lectures on Gas Theory (Dover, New York, 1995);
3.originally published in German as Vorlesunger über Gastheorie (J. A. Barth, Leipzig, 1896–1898).
4.P. and T. Ehrenfest, The Conceptual Foundations of the Statistical Approach in Mechanics (Dover, New York, 1990);
4.originally published in German in Volume IV:2:II of the Encyklopädie Der Mathematischen Wissenschaften (B. G. Teubner, Leipzig, 1912).
5.M. J. Klein, “Note on a Problem Concerning the Gibbs Paradox,” Am. J. Phys. 26, 80–81 (1958).
6.P. D. Pešić, “The principle of identicality and the foundations of quantum theory. I. The Gibbs paradox,” Am. J. Phys. 59, 971–974 (1991).
7.(a) A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer-Verlag, New York, 1992); (b) pp. 312–315.
8.P.-M. Binder and J. C. Idrobo, “Invertibility of dynamical systems in granular phase space,” Phys. Rev. E 58, 7987–7989 (1998). The invertibility of a nonlinear iterated map under computer discretization is discussed.
9.M. Hénon, “A two-dimensional mapping with a strange attractor,” Commun. Math. Phys. 50, 69–77 (1976).
10.B. L. Holian, W. G. Hoover, and H. A. Posch, “Resolution of Loschmidt’s paradox: The origin of irreversible behavior in reversible atomistic dynamics,” Phys. Rev. Lett. 59, 10–13 (1987).
11.J. L. Lebowitz, “Microscopic origins of irreversible macroscopic behavior,” Physica A 263, 516–527 (1999).
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