Our everyday experiences teach us that any imbalance like temperature gradients, non-uniform particle-densities etc. will approach some equilibrium state if not subjected to any external force. Phenomenological descriptions of these empirical findings reach back to the 19th century where Fourier and Fick presented descriptions of relaxation for macroscopic systems by stochastic approaches. However, one of the main goals of thermodynamics remained the derivation of these phenomenological description from basic microscopic principles. This task has gained much attraction since the foundation of quantum mechanics about 100 years ago. However, up to now no such conclusive derivation is presented. In this dissertation we will investigate whether closed quantum systems may show equilibration, and if so, to what extend such dynamics are in accordance with standard thermodynamic behavior as described by stochastic approaches. To this end we consider i.a. Markovian dynamics, Fokker-Planck and diffusion equations. Furthermore, we consider fluctuation theorems as given e.g. by the Jarzynski relation beyond strict Gibbsian initial states. After all we find indeed good agreement for selected quantum systems.