Hmmm... I was already thinking in the statistical version. Is there a microscopic version of the second law? It seems to me that, by what you said, it is not to be used for a small number of particles, is it?
Also, I thought energy coservation could be violated for small amounts of time...
There is something I still don't understand. You are saying that we can derive that fundamental laws must be obeyed. I thought a fundamental law would be something that would arise just by observation or some kind of
consistence. For example, general covariance is a fundamental law, isn't it...
I've just read in the first pages of The Elegant Universe that Greene believes that all fundamental laws should be contained in the microscopic domain, all other laws are derived.
Is it really so evident that the laws of thermodynamics are derived and not fundamental? The second law, is it...
I've just checked Mukhanov and Winitzki. The book is awesome and very pedagogical, not only on Hawking radiation but all over the whole chapter 9. Exactly what I was looking for. Thanks a lot for the indication.
It is quite nice indeed, but I am looking for the derivation of the effect. I did look at Hawking's original paper, but it is not very clear though, at least at my level. I was expecting something more digested once the topic is old enough to have filtered to textbooks.
I looked at Wald. It seems that it is rather involved. I will try to get the other books. In any case, if you can indicate any material that will help, I will be very grateful.