Hydrodynamics of classical and quantum active systems: From irreversibility and topology to quantum coherence

Hydrodynamics, in its classical sense, describes the dynamics of macroscopic fluids. In
condensed matter systems, it provides a powerful framework to capture the collective,
fluid-like behavior of microscopic constituents in a material that is far from equilibrium.
This thesis is dedicated to investigating some of the nonequilibrium phenomena in both
quantum and classical active systems, with a unifying emphasis on hydrodynamic ap-
proaches and a focus on the emergence of collective dynamics.
The first part of the thesis examines irreversibility in scalar active turbulence using
a hydrodynamic description in the negligible inertia limit, combined with the framework
of stochastic thermodynamics. By numerically solving the field theoretical framework
Active Model H, we quantify irreversibility via the informatic entropy production rate.
Large-scale simulation results reveal a strong spatial correlation between regions of high irreversibility and patterns and symmetries of topological defects, underscoring the pivotal role of defects in organizing irreversibility within active turbulent flows.
The second part extends to active systems in the quantum regime, an emerging field
that seeks to extend active matter concepts into domains governed by quantum mechanics. A striking example is flocking in hard-core bosons, which resembles classical flocking yet displays long-range quantum coherence, marking a genuinely quantum collective state. While this phenomenon has been numerically demonstrated, the analytical understanding of emergent coherence in the flocking phase remains incomplete. To elucidate the emergence of coherence in this phase, we develop a coarse-grained hydrodynamic theory for one-body correlation functions, which are the key measures of coherence. The resulting continuum equations, supported by both analytics and simulations, capture the emergence of quantum coherence and suggest superfluid-like transport within the quantum flocking phase.
The third part focuses on electron hydrodynamics in graphene, where, within an in-
termediate temperature regime, dominant electron-electron scattering leads to collective viscous flow of electrons. We examine how a tunable interaction such as Rashba spin–orbit coupling, which couples spin and momentum degrees of freedom, modifies the hydrodynamic flow of electrons. Our analysis shows that the interplay between RSOC strength and carrier density significantly alters the viscosity, thereby shaping the collective transport behavior of the electron fluid.
Overall, this thesis shows that hydrodynamic and coarse-grained descriptions provide
a unifying lens on diverse nonequilibrium systems, spanning active turbulence, quantum
flocking, and viscous electron flow. Particular emphasis is placed on irreversibility and
topology in classical systems, and on long-range quantum coherence in the quantum
regime of collective transport.