The Thermodynamics of Small Driven Systems

In the present thesis, a thermodynamic theory is developed for driven soft matter sys-tems like polymer solutions and colloidal suspensions. Within this theory, notions like the work applied to the system externally and the heat dissipated into a heat reservoir will be defined consistently. Going beyond mean values, all quantities are defined along a single trajectory. This thermodynamic approach is completed through a nonequilibrium generalized entropy. Recent theoretical progress has led to the formulation of a class of nonequilibrium fluc-tuation relations holding in great generality beyond the well-understood linear response regime. We derive these relations and show how they are connected to the thermody-namic quantities introduced before. Since these quantities are defined on the level of single trajectories, stochasticity of the system implies probability distributions for them. The nonequilibrium fluctuation relations like the Jarzynski relation for the work then ba-sically restrict these probability distributions. In order to obtain the still nonuniversal distribution functions, we show how these functions can be obtained through derivin