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 supernovae. 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.
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