Foundations of Stochastic Thermodynamics

Abstract: Small systems in a thermodynamic medium --- like colloids in a suspension or the molecular machinery in living cells --- are strongly affected by the thermal fluctuations of their environment. Physicists model such systems by means of stochastic processes. Stochastic Thermodynamics (ST) defines entropy changes and other thermodynamic notions for individual realizations of such processes. It applies to situations far from equilibrium and provides a unified approach to stochastic fluctuation relations. Its predictions have been studied and verified experimentally. This thesis addresses the theoretical foundations of ST. Its focus is on the following two aspects: (i) The stochastic nature of mesoscopic observations has its origin in the molecular chaos on the microscopic level. Can one derive ST from an underlying reversible deterministic dynamics? Can we interpret ST's notions of entropy and entropy changes in a well-defined information-theoretical framework? (ii) Markovian jump processes on finite state spaces are common models for bio-chemical pathways. How does one quantify and calculate fluctuations of physical observables in such models? What role does the topology of the network of states play? How can we apply our abstract results to the design of models for molecular motors? The thesis concludes with an outlook on dissipation as information written to unobserved degrees of freedom --- a perspective that yields a consistency criterion between dynamical models formulated on various levels of description.