  We show that fundamental thermodynamic relations can be derived from
deterministic mechanics for a non-ergodic system. This extend a similar
derivation for ergodic systems and suggests that ergodicity should not be
considered as a requirement for a system to exhibit a thermodynamic behavior.
Our analysis emphasizes the role of adiabatic invariants in deterministic
description and strengthens the link between mechanics and thermodynamics. In
particular, we argue that macroscopic thermodynamic behavior of a system is
caused by the existence of different time scales in its deterministic
microscopic evolution.
