*Stephen J. Blundell and Katherine M. Blundell*

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter defines some basic concepts in probability theory. It begins by stating that the probability of occurrence of a particular event, taken from a finite set of possible events, is zero if ...
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This chapter defines some basic concepts in probability theory. It begins by stating that the probability of occurrence of a particular event, taken from a finite set of possible events, is zero if that event is impossible, is one if that event is certain, and takes a value somewhere in between zero and one if that event is possible but not certain. It considers two different types of probability distribution: discrete and continuous. Variance, linear transformation, independent variables, and binomial distribution are also discussed.Less

This chapter defines some basic concepts in probability theory. It begins by stating that the probability of occurrence of a particular event, taken from a finite set of possible events, is zero if that event is impossible, is one if that event is certain, and takes a value somewhere in between zero and one if that event is possible but not certain. It considers two different types of probability distribution: discrete and continuous. Variance, linear transformation, independent variables, and binomial distribution are also discussed.

*Geoffrey Grimmett and Colin McDiarmid (eds)*

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.001.0001
- Subject:
- Mathematics, Probability / Statistics

Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and ...
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Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and inspired generations of students and researchers in mathematics. This book summarizes and reviews the consistent themes from his work through a series of articles written by renowned experts. These articles, presented as chapters, contain original research work, set in a broader context by the inclusion of review material.Less

Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and inspired generations of students and researchers in mathematics. This book summarizes and reviews the consistent themes from his work through a series of articles written by renowned experts. These articles, presented as chapters, contain original research work, set in a broader context by the inclusion of review material.

*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.