• Corpus ID: 104291954

Coconuts and Islanders: A Statistics-First Guide to the Boltzmann Distribution

@article{Zhang2019CoconutsAI,
  title={Coconuts and Islanders: A Statistics-First Guide to the Boltzmann Distribution},
  author={Brian Hu Zhang},
  journal={arXiv: Statistical Mechanics},
  year={2019}
}
  • B. Zhang
  • Published 7 April 2019
  • Physics
  • arXiv: Statistical Mechanics
The Boltzmann distribution is one of the key equations of thermal physics and is widely used in machine learning as well. Here I derive a Boltzmann distribution in a simple pedagogical example using only tools from a first-year probability course. The example is called "coconuts and islanders" and was taught to me by my father, Shoucheng Zhang (1963 - 2018), to whom these notes are dedicated. By focusing on this simple story, which can be easily simulated on a computer, I aim to provide a more… 
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References

SHOWING 1-10 OF 15 REFERENCES
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is…
Fundamentals of Statistical and Thermal Physics
This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical…
Ergodic theorem, ergodic theory, and statistical mechanics
  • C. Moore
  • Mathematics
    Proceedings of the National Academy of Sciences
  • 2015
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly…
Lectures on Gas Theory
Our goal is always to offer you an assortment of cost-free ebooks too as aid resolve your troubles. We have got a considerable collection of totally free of expense Book for people from every single…
Introduction To Monte Carlo Algorithms
These lectures that I gave in the summer of 1996 at the Beg-Rohu (France) and Budapest summer schools discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple…
Pattern Recognition and Machine Learning
TLDR
This book covers a broad range of topics for regular factorial designs and presents all of the material in very mathematical fashion and will surely become an invaluable resource for researchers and graduate students doing research in the design of factorial experiments.
An introduction to thermal physics
Preface Units, symbols and conventions 1. Temperature 2. Internal energy, heat and work 3. The ideal gas 4. Real substances 5. Interatomic forces 6. Thermal radiation 7. Heat into work Appendices…
Information Theory, Inference, and Learning Algorithms
  • D. Mackay
  • Computer Science
    IEEE Transactions on Information Theory
  • 2004
Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
Velocity Distributions in Potassium and Thallium Atomic Beams
Ergodic hypothesis in classical statistical mechanics
An updated discussion on physical and mathematical aspects of the ergodic hypothesis in classical equilibrium statistical mechanics is presented. Then a practical attitude for the justification of…
...
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