This cumulative dissertation explores the microscopic and mesoscopic dynamics of systems with broken time-reversal and parity symmetries, with a particular focus on odd-diffusive (also chiral) systems. Through a combination of first-principles theory, kinetic approaches, and statistical mechanics in the dilute limit, as well as field-theoretic approaches for crowded systems the four constituent publications provide a coherent narrative on how such symmetries, or their deliberate breaking, manifest themselves in unconventional transport phenomena. A central theme across the works is the analytical characterisation of odd-diffusive dynamics, where a transverse flux arises perpendicular to concentration gradients. In this context, the first study challenges long-standing assumptions by demonstrating that, contrary to classical expectations, the force autocorrelation function (FACF) in equilibrium systems with odd diffusion can become negative and even oscillatory, leading to enhanced self-diffusion. The second work extends this framework to non-equilibrium active chiral systems, deriving from first principles a continuum field theory for interacting active chiral particles. By incorporating steric interactions geometrically, it establishes a microscopic foundation for the Active Model B+, revealing how chirality modifies effective transport coefficients. The third work bridges these findings, employing a Fourier-mode analysis to exactly solve the propagator for interacting odd-diffusive particles. It shows how the mutual rotation and polarisation dynamics of particle pairs mechanistically underpin the previously observed oscillatory FACF behaviour. Finally, the fourth study extends the analysis to the regime of crowded systems, demonstrating that the phenomenon of enhanced self-diffusion persists even at high densities. Using a field-theoretic approach based on the Dean-Kawasaki equation, it generalises the effect to systems with non-steric interactions, and specifically considers Gaussian core particles. While all studies are unified by a focus on systems governed by antisymmetric transport tensors and resulting non-Hermitian dynamics, they differ in scope and level of description: from microscopic stochastic processes to kinetic hierarchies, and coarse-grained field theories. These differences allow the thesis to highlight the interplay between microscopic interactions and emergent macroscopic behaviour, applied to the new class of odd systems.
Erik Kalz (Thu,) studied this question.