Each thermodynamical system can be ascribed an entropy that measures the amount of ignorance about the system state. In quantum mechanics, the von Neumann entropy is completely described by the density matrix of the system.
The talk presents an exact quantum-mechanical expression for the entropy of a system in contact to a reservoir, containing entropy production and flow to the reservoir. Since the total entropy stays constant in this set-up, one can infer a negative entropy hidden in the correlations (entanglement) between system and reservoir that is exactly as large as the produced entropy. The expression for the entropy production is compared to an alternative result from the theory of open quantum systems. In a simple few-level system, the advantage of the derived expression becomes obvious, as it remains a positive quantity, while the alternative version suggests a negative entropy production.

M. Esposito, K. Lindenberg, and Ch. Van den Broeck, "Entropy production as correlation between system and reservoir", New J. Phys. 12, 013013 (2010).

In 1916 Einstein predicted with his theory of general relativity that accelerating masses emit gravitational radiation. These disturbances in the curvature of space-time that propagate like waves at the speed of light are called gravitational waves (GWs). One hundred years later in 2016 the phenomenon was directly observed for the first time by the LIGO experiment. It is of big interest to connect the observed GW events to their astrophysical origin, like binary-single systems of three black holes. The presentation gives a short introduction to Post-Newtonian Mechanics. The concept of topology of black hole binary-single interactions refers to a graphical representation of the distribution of interaction outcomes as a function of the orbital initial conditions.

Johan Samsing, Teva Ilan, "Topology of black hole binary-single interactions", Mon. N. Roy. Astron. Soc. 476(2),1548-60 (2018).

Diffusion, the stochastic motion of a particle, is usually described by the mean squared displacement (MSD). It scales linear with time for normal (Brownian) diffusion. In many systems this is violated and the MSD scales like time with an exponent. Then one speaks of anomalous diffusion. Subdiffusion is "slower" than Brownian motion and describes for example particles in crowded environments like the cytoplasm or lipid-bilayer of biological cells. Due to active motion, diffusion can be faster and is called superdiffusion. At long times both kinds of anomalous diffusion show a crossover to normal behavior if the system is finite. This can be modelled with different exponents for different time scales. To portray the cross-over region correctly, truncation, so-called tempering, can be applied and one thus gets a complete description.
Literature: D. Molina-Garcia et al. "Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers", New J. Phys. 20(10), 103027 (2018).

Symmetries of a physical system allow us to classify its properties, such as the conserved quantities in classical mechanics or the quantum mechanical states of the system. Lie groups and their associated Lie algebras are the mathematical language for the symmetries of physical systems. The presentation provides a brief introduction to Lie groups, with an example of the groups SO(3) (for rotations in three-dimensional space), SU(2) and SO(3,1) (for Lorentz transformation in Minkowski space). We illustrate the concepts of generators and structure constants of the corresponding Lie algebras, and show the strong relationship to linear transformations in physics. These groups share common mathematical structures and can be regarded as subgroups of the General Linear group each having an invariance condition.
Literature: Y. S. Kim, "Lorentz group in polarization optics", J. Opt. B: Quantum Semiclass. Opt. 2, R1-5 (2000).

Newtonian gravitational theory is linear. General relativity is strongly nonlinear and rather complex. Here an intermediate "Nonlinear Newtonian gravity" is discussed, which works without curvature. We describe a field whose sources are mass and charge, and compare with the general relativity results. As an example, we consider a charged black hole bombarded by charged particles. We determine the position of a turn-around point and critical charge/mass ratio for the non-relativistic and relativistic cases. This is an important result to predict the stability of charged black holes.
Literature: Michael R. R. Good, "On a nonlinear Newtonian gravity and charging a black hole", Am. J. Phys. 86(6), 453-59 (2018).

When analyzing a time-dependent process, one often uses the power spectral density (PSD) which is calculated with a Fourier transform in the limit of infinite observation time and taking an ensemble average. Many experiments do not have the possibility to create sufficiently large datasets for ensemble averages and also the observation time is always finite. So it is interesting to ask what information one can extract from just a single trajectory with finite observation time and what are the limits.
The talk will introduce the PSD in the framework of Brownian motion and will discuss what information can be extracted from single trajectories.
Literature: Diego Krapf, Enzo Marinari, Ralf Metzler, Gleb Oshanin, Xinran Xu and Alessio Squarcini, "Power spectral density of a single Brownian trajectory: what one can and cannot learn from it", New J. Phys. 20, 023029 (2018).

Negative absolute temperatures, a popular example being the population inversion in laser physics, are a well established concept in theoretical physics. Nevertheless, in 2013, Dunkel and Hilbert claimed that negative temperatures are only due to the often used, but in their opinion "wrong" definition of entropy, introduced by Boltzmann. Instead the Gibbs (or rather) Hertz entropy is proposed, that is supposed to solve the problem with absolute negative temperatures. We discuss this paper, the advantages and disadvantages of both entropies, and the plausibility of negative temperatures with the help of a comment on this paper.
Literature: J. Dunkel, S. Hilbert, "Consistent thermostatistics forbids negative absolute temperatures", Nature Phys. 10, 67 (2013); U. Schneider, S. Mandt, et al. "Comment on 'Consistent thermostatistics forbids negative absolute temperatures'", arXiv:1407.4127 (2014)