*Ta-Pei Cheng*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199669912
- eISBN:
- 9780191744488
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199669912.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

We discuss another of Einstein’s statistical contributions to quantum theory: his work on quantum statistics. It was prompted by a paper that S. Bose sent to him in 1924 when the physics community ...
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We discuss another of Einstein’s statistical contributions to quantum theory: his work on quantum statistics. It was prompted by a paper that S. Bose sent to him in 1924 when the physics community had finally accepted the photon idea upon the discovery and analysis of Compton scattering. We present in detail Bose’s derivation of Planck’s distribution, using a particle approach. Einstein extended Bose’s analysis of radiation to systems of matter particles. Here he made the discovery of the astounding phenomenon of Bose–Einstein condensation. The ultimate understanding of Planck’s spectral distribution came about in modern quantum mechanics with its notion of indistinguishable particles, and the connection between spin and statistics. We also provide a modern discussion of Bose–Einstein condensation.Less

We discuss another of Einstein’s statistical contributions to quantum theory: his work on quantum statistics. It was prompted by a paper that S. Bose sent to him in 1924 when the physics community had finally accepted the photon idea upon the discovery and analysis of Compton scattering. We present in detail Bose’s derivation of Planck’s distribution, using a particle approach. Einstein extended Bose’s analysis of radiation to systems of matter particles. Here he made the discovery of the astounding phenomenon of Bose–Einstein condensation. The ultimate understanding of Planck’s spectral distribution came about in modern quantum mechanics with its notion of indistinguishable particles, and the connection between spin and statistics. We also provide a modern discussion of Bose–Einstein condensation.

*Robert H. Swendsen*

- Published in print:
- 2019
- Published Online:
- February 2020
- ISBN:
- 9780198853237
- eISBN:
- 9780191887703
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198853237.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This chapter derives the part of the entropy that is generated by the positions of particles, or the configurational entropy. The remaining part of the entropy, which is generated by the momenta of ...
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This chapter derives the part of the entropy that is generated by the positions of particles, or the configurational entropy. The remaining part of the entropy, which is generated by the momenta of the particles, is derived in Chapter 6. While both derivations are unconventional, they are based directly on an 1877 paper by Boltzmann that discusses the exchange of energy between two or more systems. The dependence of the entropy on the number of particles is derived solely by assuming that the probability of a given particle being in a specified volume is proportional to that volume. No quantum mechanics is required for this derivation, and the result is valid for both distinguishable and indistinguishable particles.Less

This chapter derives the part of the entropy that is generated by the positions of particles, or the configurational entropy. The remaining part of the entropy, which is generated by the momenta of the particles, is derived in Chapter 6. While both derivations are unconventional, they are based directly on an 1877 paper by Boltzmann that discusses the exchange of energy between two or more systems. The dependence of the entropy on the number of particles is derived solely by assuming that the probability of a given particle being in a specified volume is proportional to that volume. No quantum mechanics is required for this derivation, and the result is valid for both distinguishable and indistinguishable particles.