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Prog. Theor. Phys. Vol. 22 No. 6 (1959) pp. 745-756
An Alternative Approach to the Ergodic Problem
J. M. Blatt
Research Institute for Fundamental Physics, Yukawa Hall, Kyoto University, Kyoto, Japan
and
Applied Mathematics Department, University of New South Wales, Sydney, Australia
(Received May 19, 1959)
Abstract:
The usual approach to the ergodic problem makes use of the idea of “coarse-graining”. That is, a macroscopic observer is supposed to be limited to “coarse-grained” experiments, and the resultant lack of complete information about the system gives rise to the irreversible increase of the (coarse-grained) entropy. It is shown that this approach is untenable, since macroscopic observers are not restricted in priniciple to coarse-grained experiments, and in fact one “fine-grained” experiment has already been carried out in practice. An alternative approach is presented which avoids these difficulties. The irreversible increase of entropy is due to molecules outside the system proper, which collide with the outside of the box enclosing the system; this leads to a truly random, in principle unpredictable perturbation, which can be treated only stochastically. The number of particles within the system is irrelevant for this purpose, and in particular need not be large.
URL :
http://ptp.ipap.jp/link?PTP/22/745/
DOI : 10.1143/PTP.22.745
References:
- M. R. Schafroth, unpublished manuscript and private communication.
- R. C. Tolman, “The Principles of Statistical Mechanics”, Oxford (1938).
- D. ter Haar, “Elements of Statistical Mechanics”, New York (1954).
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Hahn, Phys. Rev. 80 (1950), 580[APS]; Physics Today 6 (1953), 4.
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P. G. Bergmann and J. L. Lebowitz, Phys. Rev. 99 (1955), 578[APS].
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J. L. Lebowitz and P. G. Bergmann, Ann. of Phys. 1 (1959), 1[CrossRef].
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J. L. Lebowitz and H. L. Frisch, Phys. Rev. 107 (1957), 917[APS].
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E. P. Gross and J. L. Lebowitz, Phys. Rev. 104 (1956), 1528[APS].
- J. von Neumann, “Mathematical Foundations of Quantum Mechanics”, Dover Publications, New York (1943), Chapter V.
- M. Fierz, Helv. Phys. Acta 28 (1955), 705; see the abstract. The paper itself is concerned with coarse-graining in its usual sense.
Citing Article(s) :
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Progress of Theoretical Physics Vol. 23 No. 4 (1960) pp. 755-757
:
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An Entropy Concept in Statistical Mechanics
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Kyozi Kawasaki
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Progress of Theoretical Physics Vol. 24 No. 4 (1960) pp. 741-754
:
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Local Properties in Non-Equilibrium Systems
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J. M. Blatt
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Progress of Theoretical Physics Vol. 26 No. 5 (1961) pp. 761-789
:
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Persistent Ring Currents in an Ideal Bose Gas
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J. M. Blatt
