| This thesis has two major parts. The first part concerns studies of the equilibrium thermodynamics on different models using a self-consistent Ornstein-Zernike approximation (SCOZA). For most approximate correlation-function theories there exists an inconsistency for thermodynamic quantities evaluated from different thermodynamic routes. In SCOZA one solves this inconsistency through a renormalization procedure, which is based on the enforcement of thermodynamic consistency for quantities evaluated from the energy and the compressibility routes. This procedure has resulted in remarkable accuracy of thermodynamics for most phase regions. We apply several versions of SCOZA to study different models such as the two-dimensional lattice gas, the hard-core Yukawa fluid, and the polymer fluid. Our main objective is to develop a simple non-perturbative approximation that can give accurate results for thermodynamic quantities even when the system stays very close to its critical point.; The second part is focused on a study of the protein-folding dynamics using a statistical energy landscape theory. A protein molecule is modelled as a heterogeneous polymer with randomized interaction energies characterized by a statistical distribution. This results in an funnel-like energy landscape with local fluctuations (roughness) and an overall bias towards the folded state. With the introduction of an order parameter, the direction of folding can be characterized. The statistical energy landscape is then mapped into a one-dimensional continuous-time random walk along the order parameter, in which the dynamics is represented through a generalized Fokker-Planck equation. By solving the equation numerically we find a transition from exponential to non-exponential kinetics in the distribution of the first-passage time to the folded state. In our results the non-exponential kinetics has a distribution which resembles a truncated Levy distribution in time. |
