E. coli through obstacles: fluxes, entropy production and extractable work in active matter

Relating entropy production to underlying thermodynamic fluxes and extractable work for systems arbitrarily far from equilibrium remains a challenging problem. For systems in a non-equilibrium steady state, entropy production rate (EPR) has been studied based on the statistical irreversibility between time-forward and time-reversed trajectories of observed degrees of freedom (DOFs), both globally and, more recently, locally. Here, we explore the relation between local EPR, fluxes, and extractable work for an active matter system consisting of swimming E. coli rectified by funnel-shaped obstacles using theory, simulations, and experiments. We propose a minimal mechanical model to quantitatively capture experimentally measured local fluxes at funnel tips. We then measure irreversibility in different DOFs such as position and momentum, and show how they are related to the corresponding fluxes. Finally, we measure the local work extracted by an optically trapped colloid at a funnel tip that is weakly coupled to bacterial motion and characterize its relation to fluxes and EPR. Our work sheds light on the intrinsic relation between fluxes, irreversibility, and work in active systems far away from equilibrium.