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;
**end of part 1 of the course (see overview below)**. 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 course**.
**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.*
- Lecture 5 (April
22): Quantum teleportation, superdense coding. General
structure of quantum resource theories: free states and
operations, convexity, tensor product structure.
- Lecture 6 (April
29): The Resource Theory of Entanglement. [Some small corrections added on April
30.]
- Lecture 7 (May 6):
Asymptotic entanglement conversion, Resource monotones
& measures, entanglement monotones, entropy of
entanglement. [Some small
corrections added on May 8.]
- Lecture 8 (May
13): Passivity, thermality, and the Gibbs state.
**End of part 3 of the course.**
- Lecture 9 (May
20): Recap of passivity, definition of the resource
theory of athermality; zeroth law; heat baths unlock
state transitions; transition rates in the thermodynamic
limit: recovering the free energy. [Some small corrections added on May
25.]
- Lecture 10 (May
27): Recap of previous lecture; reducing thermal
operations to the classical case (for blockdiagonal
states only), d-majorization, d-Lorenz curves. [Some small corrections added on May
26.]
- Lecture 11 (June
3): The Rényi divergences, work cost: the max-free
energy, extractable work: the min-free energy,
approximate transitions: smoothing.
- Lecture 12 (June
10): Comparison of two resource theories; catalysis in
the RT of nonuniformity and in the RT of athermality;
the "second laws" of (quantum) thermodynamics.
- Lecture 13 (June
17): Coherence in the resource theory of athermality.
Time-translation symmetry and thermodynamics; thermal
operations versus Gibbs-preserving maps; free energy and
asymmetry monotones.
**Lecture 14**(June 24): If you have followed the course, then you will now see that you are able to read and understand**actual research papers**in the field. Start by**reading part of the following (famous) paper**: J. Åberg,*Catalytic coherence*, Phys. Rev. Lett.**113**, 150402 (2014), download here. It is enough if you read the main text (4 pages), and you can also**skip**the part on the half-infinite ladder. You should be able to understand most of what's written. After this, please**watch the talk**that I've given in this year's "Thermodynamics for Young Scientists" workshop in Bad Honnef: slides for download. On the one hand, this gives you a (hopefully) nice**recapitulation**of parts of the course with some pictures. On the other hand, it explains some of my own research (on catalysts, correlations and the free energy), and relates this as well to Åberg's paper.
There are 10 sheets in total. If you hand in an exercise after the due date, then we will mark it for your
information, but the points will not be counted.Some problem sets include optional parts. Points on these questions count as bonus points. When determining the percentage of points on a given problem set, these bonus points count in the enumerator, but not in the denominator. In this way, you can achieve more than 100% on some of the problems sets. - 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**) Here is a sample solution for Exercise 4.5 for download (thank you to Emanuel Schwarzhans!). - Week 5 (hand in
until
**Thursday, April 30**) Here is a solution sketch for Exercise 5.1 for download. - Week 6 (hand in
until
**Thursday, May 7**) [Corrections added on Mai 8 - the two states in Exercise 6.3(iv) had to be named the other way around] See this Mathematica notebook for Exercise 6.3(v) for download, and solution sketches for Problems 6.1 and 6.4.
- Week 7 (hand
in until
**Thursday, May 14)**[Small correction on May 20: Problem 7.4(iv)b was very difficult without an extra hint (one has to use the joint convexity of the relative entropy). We have now added this hint, and we have given full points to all students who have seriously attempted to solve this problem.] - Week 8 (hand
in until
**Thursday, May 21)**Here is a solution sketch for Exercise 8.3.iv for download.
- Week 9 (hand
in until
**Thursday, May 28)** - Week 10 (hand
in until
**Thursday, June 4)** - Week 11 (hand
in until
**Thursday, June 18 -- note one week more time)**[Small correction added on June 17.]
Last edit: June 20, 2020 |