We discuss research done in two important areas of nonequilibrium statistical
mechanics: fluctuation dissipation relations and dynamical fluctuations. In
equilibrium systems the fluctuation-dissipation theorem gives a simple relation
between the response of observables to a perturation and correlation functions
in the unperturbed system. Our contribution here is an investigation of the
form of the response function for systems out of equilibrium. Furthermore, we
use the theory of large deviations to examine dynamical fluctuations in systems
out of equilibrium. In dynamical fluctuation theory we consider two kinds of
observables: occupations (describing the fraction of time the system spends in
each configuration) and currents (describing the changes of configuration the
system makes). We explain how to compute the rate functions of the large
deviations, and what the physical quantities are that govern their form.Comment: PhD thesis (defended in may 2010
