Abstract
After a short review of the relevance of statistical physics for the description of nanoparticles and an introduction to fluctuations, the chapter presents three of the most used partition functions used in statistical physics: the microcanonical, the canonical and the grand canonical. The presentation is based on the concept of entropy or equivalently the level density which is used to define the temperature and derive the Boltzmann. Free energies and the chemical potential are introduced.
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Notes
- 1.
E. Schrödinger, Statistical Thermodynamics, The Syndics of the Cambridge University Press, 1952.
- 2.
The term ‘on the order of’, indicated by the symbol ∼, is used to describe an approximate relationship between quantities and indicates the leading order term without any attempt to determine dimensionless numerical constants. As an example, the volume of a sphere is on the order of the radius cubed.
- 3.
Some frequently used constants of nature are given in Appendix B.
- 4.
‘Then, shalt thou count to three, no more, no less. Three shalt be the number thou shalt count, and the number of the counting shalt be three.’ Monty Python and the Holy Grail.
- 5.
It is tempting but probably wasted effort to suggest to rename this ‘the nanocanonical partition function’ and ‘the nanocanonical ensemble’.
- 6.
Landau and Lifshitz disagree with this statement and derive results for temperature fluctuations. Our derivation of a canonical temperature renders fluctuations impossible. Heated discussions (pun intended) erupt on this subject in the literature from time to time.
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Hansen, K. (2013). Introduction. In: Statistical Physics of Nanoparticles in the Gas Phase. Springer Series on Atomic, Optical, and Plasma Physics, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5839-1_1
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DOI: https://doi.org/10.1007/978-94-007-5839-1_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5838-4
Online ISBN: 978-94-007-5839-1
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