| dc.description.abstracteng | The microscopic world of atoms and molecules is continuously in motion, which is manifested on the macroscopic scale as a non-zero temperature. Due to collisions with surrounding molecules that perform thermal motion, many small systems undergo erratic, random motion, known as Brownian motion. In the presence of external forces, this motion is described by the Langevin equation, which forms a basis for studying thermodynamics of stochastic systems, and proved successful in biology, physics, chemistry and beyond. In particular, unlike classical thermodynamics, the Langevin description applies to systems far from thermal equilibrium, which is, e.g., vital to approach biological processes in living systems.
In this thesis, we investigate properties of stochastic dynamics by applying the mathematical framework of stochastic calculus, that directly addresses the notion of fluctuating trajectories. The major part of the thesis is concerned with fluctuations of time-averaged observables. We derive expressions for the variance and correlations of empirical densities and currents, which are observables central to statistical mechanics on the level of individual trajectories. Based on these results, we uncover the essential role of coarse graining in space, and explain the results by connecting them to a generalized time-reversal symmetry in non-equilibrium steady states. In particular, we use the stochastic-calculus approach to rederive an inequality called thermodynamic uncertainty relation, that allows to infer entropy production from measurements of time-averaged currents. Based on our simplified derivation, we are able to systematically determine when this inequality becomes saturated, i.e.,
when the thermodynamic inference is optimal.
Another large part of the thesis investigates how systems prepared at different temperatures relax to the temperature of the environment. While the classical laws of thermodynamics only apply close to thermal equilibrium and predict a relaxation that is indifferent with respect to the sign of the temperature change, it was recently found that for large temperature differences, i.e.,
far from equilibrium, thermal relaxation becomes asymmetric, and heating is faster than cooling. In a collaboration, we experimentally confirm this asymmetry, generalize this framework, and extend the study to relaxation towards
non-equilibrium steady states.
Finally, we also address motion beyond Langevin dynamics, namely two-state dynamics that switches stochastically between different states of motion. We make predictions for experimentally relevant observables for diverse physical models, and apply the results to particle tracking data recorded in living cells.
Altogether, in this thesis, we study stochastic dynamics of systems far from thermal equilibrium. We push forward the framework of stochastic calculus to handle and understand randomly fluctuating trajectories, and to deduce thermodynamic insights and properties of experimentally relevant observables from this intrinsically stochastic dynamics. | de |