📝 SummarXiv

Abstract

For equilibrium hard spheres the stochastic geometry of the insertion space, the room to accommodate another sphere, relates exactly to the equation of state. We begin to extend this idea to active matter, analyzing insertion space for repulsive active particles in one and two dimensions using both on- and off-lattice models. In 1D we derive closed-form expressions for the mean insertion cavity size, cavity number, and total insertion volume, all in excellent agreement with simulations. Strikingly, activity increases the total insertion volume and tends to keep the insertion space more connected. These results provide the first quantitative foundation for the stochastic geometry of active matter, and opens up a new route to building a thermodynamics of active systems.