VU: Resource theories and thermodynamics
(March 11 - June 24, 2020) Lecturers: Dr. Markus P. Müller,
Dr.
Andrew J. P. Garner, Dr.
Felix Binder. (drawing and copyright by Lidia del Rio)
A final request:
- Lecture 1 (March
11),
*Overview on the lecture series; folklore derivation of Landauer's principle; basics of mixed quantum states and entropies; some exercises.*
- Lecture 2 (March
18),
*A rigorous version of Landauer's Principle; motivation for and definition of the resource theory of nonuniformity.*See also this excellent essay on the Szilard engine by Andy Garner.
- Lecture 3 (March
25),
*Majorization and Lorenz curves, nonuniformity (N.U.) monotones, distillable N.U. and N.U. of formation, the trace distance, smooth entropies.*
- Lecture 4 (April
1),
*Approximate formation/distillation of pure bits, state conversion in the thermodynamic limit, typical subsets, asymptotic equipartition property, Shannon's noiseless coding theorem.***End of part 2 of the lecture**(see overview below).
**Note**: Section 2.12 (Typical subsets, AEP, data compression) is**optional**! You don't need to understand this for the rest of the lecture or the exercises. I'm giving you an overview on these topics because they are the reason why the smoothed Rényi-0 and Rényi-infinity entropies converge to the "standard" Shannon entropy in the limit. In other words: information theory and data compression are the reason why we will recover the standard thermodynamic laws in the thermodynamic limit. For those of you who want to know more, here are some possible references: -- Cover, Thomas,*Elements of Information Theory*, John Wiley & Sons, 2006. (Well-known and well-written book on the basics of information theory) -- The Wikipedia entry (oh well, yes, indeed). -- Shannon's original 1948 paper. Note that**"AEP" is for "asymptotic equipartition property"**: the property that typical outcome sequences, in the limit of large n, will all have approximately the "same" probability (close to 2^(-nH)). It is also the name of our lemma in Section 2.10, because it's mathematically closely related.
- Weeks 1 and 2
(hand in until
**Tuesday, March 24**) A solution sketch for Problem 2.2 can be found here.
- Week 3 (hand in
until
**Thursday, April 2**) Here are sample solutions for download (thank you to Lorenz Hummer for supplying them!)
- Week 4 (hand in
until
**Thursday, April 23**)
Last edit: April 7, 2020 |