I am having trouble in understanding the following concepts :
Pg 231 Appendix B of the link http://books.google.ca/books?id=lEu7CTGjdDkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=entropy&f=false which is of the book Chaos and the Evolving Universe by Sally J. Goerner mentions that Entropy $S$: $$ S = \ln V $$ where $V$ is the phase space volume. According to the book, this equation is from the concept of Boltzmann's entropy.
(Q1) How is This equation coming? How can we say that entropy = log of phase space volume? References and explanation would be appreciated. According to the book, the Bolzmann's constant, $k_B$, is taken to be $1$. But actually there is a value to the constant. Can I take the Boltzmann constant to be equal to $1$?
Also, if the entropy increases, does this mean that the volume decreases?
(Q2) Secondly, can Kolmogorov entropy, from Information theory be stated as logarithm of phase space volume that is equivalent to entropy from statistical mechanics? I am unsure if I can replace Boltzman with Kolmogorov Sinai (KS) entropy.
(Q3) What is the difference between Gibb's entropy and Shannon's entropy since the formula http://en.wikipedia.org/wiki/Entropy_%28statistical_views%29 is the same.