Analytical and Kinetic Monte Carlo Investigation of Stochastic Networks: Closed Systems and Absorbing State Dynamics

This diploma thesis investigates the dynamical properties of stochastic networks represented by discrete states with known transition rate constants. The research focuses on establishing a comprehensive framework that combines analytical solutions with Kinetic Monte Carlo (KMC) simulations to characterize the time evolution of these systems. The study will specifically address two distinct regimes: closed systems where the detailed balance condition is satisfied and the rate constant matrix is stochastic, leading to a well-defined equilibrium; and open systems featuring absorbing states along their boundaries, which model irreversible processes such as physical aging of glasses. By rigorously comparing the KMC trajectories against the analytical master equation predictions, the project aims to validate the numerical approach and explore the statistical behavior of transition times and survival probabilities in non-equilibrium conditions. This work will provide insights into the reliability of kinetic simulations for complex networks and contribute to the theoretical understanding of both equilibrium relaxation and first-passage phenomena in stochastic processes.