  This thesis investigates the connection between quantum theory,
thermodynamics and information theory. Theories with structure similar to that
of quantum theory are considered, mathematically described by the framework of
"Generalized Probabilistic Theories". For these theories, a thought experiment
by von Neumann is adapted to obtain a natural thermodynamic entropy definition,
following a proposal by J. Barrett. Mathematical properties of this entropy are
compared to physical consequences of the thought experiment. The validity of
the second law of thermodynamics is investigated. In that context, observables
and projective measurements are generalized to prove an entropy increase for
projective measurements of ensembles. Information-theoretically motivated
definitions of the entropy are compared to the entropy from the thermodynamic
thought experiment. The conditions for the thermodynamic entropy to be
well-defined are considered in greater detail. Several further properties of
the theories under consideration (e.g. whether there is higher order
interference, Pfister's state discrimination principle) and their relation to
entropy are investigated.
