  We consider the micro-canonical ensemble of a classical Hamiltonian dynamical
system, the Hamiltonian being parameter dependent and in the possible presence
of other first integrals. We describe a thermodynamic formalism in which a 1st
law of thermodynamics, or fundamental relation, is based upon the bulk-entropy,
S. Under an ergodic hypothesis, S is shown to be an adiabatic invariant.
Expressions for derivatives and thermodynamic relations are derived within the
micro-canonical ensemble itself.
