The idea which started this work is that the relation between dynamics and thermodynamics can be based on the concepts of energy and work, which are common to both fields. The work done by a quantum or classical Hamiltonian system is defined through the re-sponse of the system to cyclic changes in a set of time-dependent macroscopic external fields. The entropy of a state is then defined in such a way that it is simply related to the available work. This means that it is described completely in terms of dynamical quantities. A consequence of this definition is that there can be a unique, intrinsic entropy only if its value is constant in time for a closed system. Hence, there is no intrinsic irreversibility in this formalism. Instead, there is a family of non-trivial entropy functions, one for each set of thermodynamic pro-esses allowed by the experimenter's control of the system through the external fields.
The present approach is closely modelled on a type of experi-ment where the relaxation properties are probed by modern tech-niques which provide a high time resolution. The fact that such experiments were not possible at the time when non-equilibrium statistical mechanics was in its infancy has influenced its de-velopment up to the present. A result is that the standard types of rigorous mathematical treatment, as for example that given by ergodic theory, provide a rather tenous relation between the basic concepts and the experimentally accessible quantities. In this work I have tried to improve on this situation. There is, for in-stance no a priori information-theoretic interpretation of the entropy for non-equilibrium states, as this is not relevant for the given set of experiments.