Active pressure and local entropy production of bacterial suspensions

The mechanical pressure of active matter cannot be trivially related to other thermodynamic quantities, unlike systems in equilibrium. For systems in a non-equilibrium steady state, entropy production rate (EPR) has recently been studied based on the statistical irreversibility between time-forward and time-reversed trajectories of observed degrees of freedom, both globally and locally. Here, we explore the relation between the local mechanical pressure and local EPR of active bacterial suspensions. By means of experiments and Brownian dynamics simulations, we characterize the correlation between local active pressure and local EPR for swimming bacteria rectified by funnel-shaped geometries. While the active pressure is measured in experiments by tracking the displacement of a tracer particle held by optical tweezers at the tip of the funnel, the local EPR is calculated from the Kullback-Leibler divergence of the discretized sequence of collisions with the tracer particle. We further develop a simple theoretical model, which quantitatively captures the relation between active mechanical pressure and local EPR. Our study reveals the intrinsic relation between active pressure and the time irreversibility of nonequilibrium systems.