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  • Print publication year: 2017
  • Online publication date: November 2017

Appendix A - Notes

Summary

Chapter 1

[1](p. 4) The property described in (1.1) is usually referred to as additivity rather than extensivity. Extensivity of the energy is often valid and equivalent to additivity in the thermodynamic limit, at least for systems with finite-range interactions, as considered usually in this book. For systems with long-range interactions, extensivity does not always hold.

[2](p. 20) This terminology was introduced by Gibbs [137], but the statistical ensembles were first introduced by Boltzmann under a different name (ergode for themicrocanonical ensemble and holode for the canonical).

[3](p. 21)We adopt here the following point of view explained by Jaynes in [181]:

This problem of specification of probabilities in cases where little or no information is available, is as old as the theory of probability. Laplace's “Principle of Insufficient Reason” was an attempt to supply a criterion of choice, in which one said that two events are to be assigned equal probabilities if there is no reason to think otherwise.

Of course, some readers might not consider such a point of view to be fully satisfactory. In particular, one might dislike the interpretation of a probability distribution as a description of a state of knowledge, rather than as a quantity intrinsic to the system. After all, there is amore fundamental theory and it would be satisfactory to derive this probability distribution from the latter. Many attempts have been done, but no fully satisfactory derivation has been obtained. We will not discuss such issues further here, but refer the interested reader to the extensive literature on this topic; see for example [130].

[4](p. 22) Historically, the entropy of a probability density had already been introduced by Gibbs in [137].

[5](p. 39) In our brief description of a ferromagnet and its basic properties, we are neglecting many physically important aspects of the corresponding phenomena. Our goal is not to provide a faithful account, but rather to provide the uninitiated readerwith an idea of what ferromagnetic and paramagnetic behaviors correspond to. We refer readers who would prefer a more thorough description to any of the many books on condensed matter physics, such as [1, 14, 65, 356].