Density mean back relaxation: Analytical solutions, properties, and application in experiments

The breakdown of time reversibility is one of the key concepts that distinguishes non-equilibrium from equilibrium systems. However, detecting it from experiments can be challenging. One method that allows to do so in systems with a confining potential is the recently introduced mean back relaxation (MBR). In this thesis, we demonstrate that the MBR for densities (dMBR) is an extension of the MBR that enables the detection of broken time-reversal symmetry, even in systems without a confining potential. For systems with a finite number of particles that are described by a microscopic density, we additionally find a lower bound on entropy production. We provide analytical expressions of the dMBR for Gaussian example systems of both microscopic and macroscopic densities and find good agreement with results from simulations. Evaluating experimental data, we demonstrate that the dMBR can detect activity in biological cells with a confidence of 2σ. In addition, the derived entropy bounds detect non-zero entropy production. Finally, we look at the MBR of intensities obtained from scattering (iMBR), extending the applicability of the MBR to detect broken time-reversal symmetry to scattering experiments.