  The computation of the thermodynamic properties of nuclear matter is a
central task of theoretical nuclear physics. The nuclear equation of state is
an essential quantity in nuclear astrophysics and governs the properties of
neutron stars and core-collapse supernov\ae. The framework of chiral effective
field theory provides the basis for the description of nuclear interactions in
terms of a systematic low-energy expansion. In this thesis, we apply chiral
two- and three-nucleon interactions in perturbative many-body calculations of
the thermodynamic equation of state of infinite homogeneous nuclear matter. The
conceptual issues that arise concerning the consistent generalization of the
standard zero-temperature form of many-body perturbation theory to finite
temperatures are investigated in detail. The structure of many-body
perturbation theory at higher orders is examined, in particular concerning the
role of the so-called anomalous contributions. The first-order nuclear
liquid-gas phase transition is analyzed with respect to its dependence on
temperature and the neutron-to-proton ratio. Furthermore, the convergence
behavior of the expansion of the equation of state in terms of the isospin
asymmetry is examined. It is shown that the expansion coefficients beyond the
quadratic order diverge in the zero-temperature limit, implying a nonanalytic
form of the isospin-asymmetry dependence at low temperatures. This behavior is
associated with logarithmic terms in the isospin-asymmetry dependence at zero
temperature.
