Entropy Scaling Laws in Self Propelled Glass Formers

Abstract

Predicting transport from equilibrium structure is a challenging problem in liquid state physics. Here we probe a glass forming liquid composed of self-propelled "active" particles and show that increasing the duration of self-propulsion ${\tau }_p$ makes the pair excess entropy $S_2$ more negative, thereby reducing the number of accessible configurations per particle. At moderate values of effective temperature $T$, the self-diffusivity is Arrhenius and in a reduced form obeys a Dzugutov like scaling law $D^{\ast }\sim e^{\alpha S_2}$, directly yielding us the scaling formula $S_2\sim -1/T$. In the strongly super-cooled regime, Dzugutov law does not apply and the entropy follows a power law $S_2\sim -1/T^{\beta }$ all the way up to the glass transition $T_g$. To demonstrate generality, we set the particle interactions to be purely repulsive (PR) in one case and Lennard-Jones (LJ) in the other, and find that in both the cases, the reported scaling laws are robust over three decades of variation in ${\tau }_p$. Our results may apply to transport in active colloidal suspensions, passive tracers in bacterial baths, and self-propelled granular media, to mention a few.