Stability of the Canonical Ensemble

  • George D.J. Phillies
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


An average over an N-particle canonical ensemble may be written (23.1)


Phase Space Statistical Weight Ensemble Average Canonical Ensemble Phase Point 
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  1. [1]
    In the author’s experience, a respectable fraction of all students have been brainwashed into the belief that the entropy always increases with increasing time. This belief about entropy implies that S is not a constant. The same students simultaneously believe in the existence of steam tables that report S of a volume of steam, without reporting the hour and date for which that S is presented. The existence of steam tables means that S is indeed a constant. After all, if S always increased with increasing time, there could only be one instant in all history at which a particular set of steam tables would be correct. Sentences 2 and 3 of this paragraph are logically inconsistent but both believed to be true at the same time, a state of affairs technically known as “cognitive dissonance”. Cognitive dissonance can be very hard to remove. Cognitive dissonance is a primary tool of politicians across America. The belief that entropy always increases appears to correspond to students who were taught the pernicious “Gambler’s Three Laws of Thermodynamics”, namely “1. You can’t win. 2. You can’t break even. 3. You must play.” A person who understands thermodynamics will recognize the symbolic representation of the three laws by these statements. In the experience of the author, the Gambler’s three laws of thermodynamics are astonishingly insidious, so that it is almost impossible to cause a student who has first memorized these laws to later gain any correct understanding of equilibrium thermodynamics.Google Scholar
  2. [2]
    J. W. Gibbs, Elementary Lectures in Statistical Mechanics, Yale University Press, New Haven, CT (1902), Chapter 1.Google Scholar
  3. [3]
    Strictly speaking, in a true hard-sphere system phase space motions are not continuous. As a result of collisions, hard spheres instantaneously change their velocities to new values, causing the motion of hard-sphere phase space points to be discontinuous. However, in the real world there are no true hard-sphere systems. In any real system that is approximated by the hard-sphere system, the motion of phase-space points is continuous.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • George D.J. Phillies
    • 1
  1. 1.Department of Physics and Associated Biochemistry FacultyWorcester Polytechnic InstituteWorcesterUSA

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