The Okinawa Lectures on Entropy
- Published
- Source
- arXiv
- Paper number
- 917
- Field
- Research
- arXiv ID
- 2608.14523
Key points
- The lectures explain, from a historical perspective, how Clausius, Boltzmann, Gibbs, Einstein, von Neumann, Shannon, Rényi, and Kolmogorov expanded the concept of entropy.
- Classical entropy is explained as a quantity that captures how quickly the probability of large fluctuations falls with sample size, with the discussion centered on the Sanov, Cramér, Gartner-Ellis, and Varadhan theorems.
- It explains that in classical and quantum hypothesis testing, if one type of error is constrained, the other error decreases at a rate given by relative entropy.
- It moves from von Neumann and Umegaki entropy for finite quantum states to the construction of Araki and Uhlmann relative entropy in arbitrary von Neumann algebras.
- Finally, it connects classical Kolmogorov-Sinai entropy with quantum dynamical entropy, and the author notes that there is no new material except for the organization of the material, the approach, and some proofs, while thermodynamics and black-hole applications are not covered.
Paper links
External research summaries. These are not HDATF publications or measured product results.