Generalized relationship between effective forces and active particle microstructure

Establishing a robust link between microscopic structure and effective forces in active systems remains a fundamental challenge. Recently, Paul et al. [Phys. Rev. Lett. 129, 058001 (2022)0031-900710.1103/PhysRevLett.129.058001] achieved a significant theoretical breakthrough by developing a framework based on active stress. This framework enables the computation of forces exerted by active particles on a tightly constrained probe. Nevertheless, the pronounced sensitivity of depletionlike forces in active baths to external constraints offers an opportunity to extend this theoretical framework. Using simulations, we systematically investigate this constraint dependence and uncover key discrepancies between theory and numerical results. By incorporating a constraint-dependent correction factor into the existing theory, our results align remarkably well with simulations across extensive parameters. Our findings advance the theoretical understanding of depletionlike forces in active matter and offer direct implications for experimental validation.