Contents


1. Thermodynamic entropy and Shannon entropy.
One upon a time there were two entropies .. (thermodynamic entropy and
Shannon entropy in information theory).
The 'measure' of information. From the measure of information to
thermodynamic entropy.
Informational derivation of Sackur-Tetrode equation.

2. Entropy bounds.
A bound for entropy ? A bound which scales as the area of the system ?
How can it be that a limit can be given to the amount of information that
can be stored in a piece of matter, that is to its true thermodynamic
entropy, when by no way we can state to know the ultimate structure of
matter constituents at the deepest level ? What does it mean an
area-scaling bound ?

3. Extensivity and Gibbs-Duhem relation.

4. Thermodynamics in curved spacetime.

5. Entropy for gravitating systems.
For gravitating systems, entropy does not scale as system's size.
Non-extensivity: of what, and in what sense. Systems, which entropy scales
as the area, and are not black holes.

6. Bekenstein bound.

7. Holographic bound, and holographic principle.

8. Lightsheets. Covariant entropy bound.

9. Generalised covariant entropy bound.
Connections between this bound and the others and between this bound and
the generalised 2^ law.

10. Raychaudhuri equation.

11. Sufficiency conditions for the covariant entropy bound and for its
generalised form. Proofs.

12. Local Rindler horizons.

13. Thermodynamics of spacetime.
Einstein's equations as 1^ law of thermodynamics.

14. Proof of the generalised bound in terms of local Rindler lightsheets.

15. An if and only if condition; the scale l*.

16. Generalised bound and quantum mechanics.
Coming to the formula for the entropy of black holes through l*, i.e. with
an alternative approach, with no reference to horizon temperature.

17. Proof of Bekenstein bound in terms of l*.

18. Universal bound to dynamical relaxation times.
Connection between l* and the bound to relaxation times of perturbed
thermodynamic systems (Hod's bound); time-discretisation also, in addition
to space-discretisation. Conventional systems (i.e. not black holes) which
do reach this bound.

19. eta/s.
Connection between l* and the bound to viscosity/entropy (KSS bound);
the case of a very low-viscosity fluid: the quark-gluon plasma.

20. Spacetime geometry from information ?


To Alessandro Pesci Homepage