Remark on the entropy production of adaptive run-and-tumble chemotaxis

Chemotactic active particles, such as bacteria and cells, exhibit an adaptive run-and-tumble motion, giving rise to complex emergent behaviors in response to external chemical fields. This motion is generated by the conversion of internal chemical energy into self-propulsion, allowing each agent to sustain a steady-state far from thermal equilibrium and perform works. The rate of entropy production serves as an indicates of how extensive these agents operate away from thermal equilibrium, providing a measure for estimating maximum obtainable power. Here we present the general framework for calculating the entropy production rate created by such population of agents from the first principle, using the minimal model of bacterial adaptive chemotaxis, as they execute the most basic collective action — the mass transport.