  This paper addresses fundamental aspects of statistical mechanics such as the
motivation of a classical state space with spontaneous transitions, the meaning
of non-equilibrium in the context of thermalization, and the justification of
these concepts from the quantum-mechanical point of view. After an introductory
part we focus on the problem of entropy production in non-equilibrium systems.
In particular, the generally accepted formula for entropy production in the
environment is analyzed from a critical perspective. It is shown that this
formula is only valid in the limit of separated time scales of the system's and
the environmental degrees of freedom. Finally, we present an alternative simple
proof of the fluctuation theorem.
