I often think about the phase space with quite deep interpretations. For example, contraction of phase space means losing energy. But, some of the energy is easily restored (free energy?) while some other is hard to restore (enthalpy, internal energy). This is like dividing the phase space to flexible and rough?


Are my insights correct or maybe they can be easily extended more?


**Are there any books with such interpretation-like approach to phase space and dynamical systems?**



Deeper meanings of Phase Space -- any books?
For your kind of reflections I think a useful reference could be the fantastic ["The structure of dynamical systems. A symplectic view of physics"](http://books.google.it/books?hl=it&lr=&id=4tBrbryIKQAC&oi=fnd&pg=PR17&dq=the+structure+of+dynamical+systems&ots=tVBfnMVnPn&sig=Pzi0dGmzfTSXkEh8wOFomIp3ngA#v=onepage&q&f=false) of Jean Marie Souriau.
In particular take a look at his fourth chapter "Mecanique statistique".


