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?