Electro-mechanical excitation waves in the heart may exhibit different spatio-temporal dynamics ranging from repeated plane waves to scroll waves or spatio-temporal chaos, resulting in life threatening arrhythmias. This kind of chaotic dynamics in excitable cardiac media is often characterised by significant complexity fluctuations (including laminar phases) and can be non-persistent exhibiting supertransients, with lifetimes of the chaotic phases increasing exponentially with the system size. Terminating or at least shortening chaotic transients can be life saving in the medical context of cardiac arrhythmias. Therefore, we study the impact of perturbations on the duration of transients and features of the terminal phase of chaotic transients. Practically, such perturbations can be applied via so-called virtual electrodes where electrical heterogeneities of the cardiac muscle act as local excitation sites when subjected to a global electric field. In the talk we shall present novel results on the nonlinear dynamics of the heart including features of the terminal phase of transient chaos, parameter and state estimation, as well as experimental studies and modalities.
For the macroscopic world, classical thermodynamics formulates the laws governing the transformation of various forms of energy into each other. Stochastic thermodynamics extends these concepts to micro- and nano-systems embedded or coupled to a heat bath where fluctuations play a dominant role. Examples are colloidal particles in time-dependent laser traps, single biomolecules manipulated by optical tweezers or AFM tips, and transport through quantum dots. For these systems, exact non-equilibrium relations like the Jarzynski relation, fluctuation theorems and, most recently, a thermodynamic uncertainty relation have been discovered. First, I will introduce the main principles and show a few representative experimental applications. In the second part, I will discuss the universal trade-off between the thermodynamic cost and the precision of any biomolecular, or, more generally, of any stationary non-equilibrium process. By applying this thermodynamic uncertainty relation to molecular motors, I will introduce the emerging field of "thermodynamic inference" where relations from stochastic thermodynamics are used to infer otherwise yet inaccessible properties of (bio)physical and (bio)chemical systems.