Irreversiblity in Bacterial Turbulence: Insights from the Mean-Bacterial-Velocity Model

We use the mean-bacterial-velocity model to investigate the \textit{irreversibility} of two-dimensional (2D) \textit{bacterial turbulence} and to compare it with its 2D fluid-turbulence counterpart. We carry out extensive direct numerical simulations of Lagrangian tracer particles that are advected by the velocity field in this model. We demonstrate how the statistical properties of these particles help us to uncover an important, qualitative way in which irreversibility in bacterial turbulence is different from its fluid-turbulence counterpart: For large but negative (or large and positive) values of the \textit{activity} (or \textit{friction}) parameter, the probability distribution functions of energy increments, along tracer trajectories, or the power are \textit{positively} skewed; so irreversibility in bacterial turbulence can lead, on average, to \textit{particles gaining energy faster than they lose it}, which is the exact opposite of what is observed for tracers in 2D fluid turbulence.