Bacteria Through Obstacles: Unifying Fluxes, Entropy Production, and Extractable Work in Living Active Matter

Thermodynamic equilibrium is a unique state characterized by time-reversal symmetry, which enforces zero fluxes and prohibits work extraction from a single thermal bath. By virtue of being microscopically out of equilibrium, active matter challenges these defining characteristics of thermodynamic equilibrium. Although time irreversibility, fluxes, and extractable work have been observed separately in various non-equilibrium systems, a comprehensive understanding of these quantities and their interrelationship in the context of living matter remains elusive. Here, by combining experiments, simulations, and theory, we study the correlation between these three quantities in a single system consisting of swimming Escherichia coli navigating through funnel-shaped obstacles. We show that the interplay between geometric constraints and bacterial swimming breaks time-reversal symmetry, leading to the emergence of local mass fluxes. Using an harmonically trapped colloid coupled weakly to bacterial motion, we demonstrate that the amount of extractable work depends on the deviation from equilibrium as quantified by fluxes and entropy production. We propose a minimal mechanical model and a generalized mass transfer relation for bacterial rectification that quantitatively explains experimental observations. Our study provides a microscopic understanding of bacterial rectification and uncovers the intrinsic relation between time irreversibility, fluxes, and extractable work in living systems far from equilibrium.