## 宇宙的热寂和文明的宿命

Entropy in an Expanding Universe by Steven Frautschi, Science, New Series, Vol. 217, No. 4560 (Aug. 13, 1982), pp. 593-599
http://www.informationphilosopher.com/solutions/scientists/layzer/Frautschi_Science_1982.pdf

1. 有引力的系统，熵最大的状态不是物质均一分布在空间内，而是形成一个黑洞。
2. 和封闭无引力的平衡系统的熵不同，有引力、膨胀的系统的熵不守恒，可以一直增加。
3. Relaxiation time太长。随着宇宙膨胀，causal region反而是距离平衡态越来越远了。这是因为黑洞的形成速度赶不上视界线的膨胀速度。
4. 因此膨胀的宇宙永远不会到达热寂，如果没有文明去影响它的话。
5. 一个文明通过不断收集物质并扔进一个大黑洞，并使用霍金辐射的free energy，可以获得无穷的能量。但是单位时间能够获得的能量越来越少，接近于零。文明不得不通过休眠来等待下一次活动的能量积攒起来。虽然休眠越来越漫长，只要我们足够耐心，总还是能获得任意多的能量。经典物理下的文明得以永生。
6. 考虑各种量子效应，却无法永生。基于固体的生物会有各种量子隧穿（例如原子的衰变、核聚变甚至直接变成黑洞）破坏，所以要不断修补自己。量子效应造成破坏的概率虽然非常低，但是还是会超过黑洞提供能量的速率，最终造成固体形式生物的灭亡。

## Learning Supersymmetry and Supergravity

Supersymmetry DeMYSTiFied
For very beginners, Supersymmetry DeMYSTiFied is actually an outstanding book. It has lots of details of computations, slow-paced, crystal clear explanations from both high point of views and concrete physical images.

A Supersymmetry Primer
A Supersymmetry Primer by S. R. Martin is a classic. The first half of these notes provide a very clear introduction to N=1 supersymmetry. The second half is mostly phenomenology.

Introduction to Supergravity
Introduction to Supergravity by H. Samtleben is much shorter than most of other notes I found. I finished the 29 pages in one day. These notes offer a nice introduction to N=1, D=4 supergravity and sketched other supergravity theories. They are very friendly to beginners with lots of details of the lengthy calculation of SUGRA.

Cambridge Lectures on Supersymmetry and Extra Dimensions
A combo of lecture videos of Part III course Supersymmetry and Extra Dimensions by Fernando Quevedo, and its notes. The lectures and notes are simply great for learning SUSY. arXiv:1011.1491

## Beta Function and Weyl Anomaly in String Theory

Recently I did some study on one-loop Weyl anomaly in string theory. This is actually a good topic for a student in string theory to practice loop calculations. It helps you learn general relativity in its perturbative form as well.

To name a few useful references here:

David Tong's notes on string theory

Two papers on this topic:

Strings in background fields, by Callan et al., Nucl.Phys. B262 (1985) 593

String theory effective actions, by Callan et al., Nucl.Phys. B278 (1986) 78

Low energy effective actions from String Theory by Sam Guns

## Two quotes on how to read a book in mathematics

I saw these two well said quotes from the discussion on Math Stack Exchange.

Axler, in the preface of his linear algebra book:

"You cannot expect to read mathematics the way you read a novel. If you zip through a page in less than an hour, you are probably going too fast."

Saharon Shelah, in "Classification Theory and the Number of Non-Isomorphic Models"; quoted in Just and Weese, "Discovering Modern Set Theory I":

So we shall now explain how to read the book. The right way is to put it on your desk in the day, below your pillow at night, devoting yourself to the reading, and solving the exercises till you know it by heart. Unfortunately, I suspect the reader is looking for advice on how not to read, i.e. what to skip, and even better, how to read only some isolated highlights.

## 很好的超对称场论入门教材：Supersymmetry DeMYSTiFied

Up to a multiplicative constant, there is only one possibility to try ...