$NVU$ view on energy polydisperse Lennard-Jones systems

Abstract

When energy polydispersity is introduced into the Lennard-Jones (LJ) system, there is little effect on structure and dynamics [Ingebrigtsen and Dyre, J. Phys. Chem. B 127, 2837 (2023)]. For instance, at a given state point both the radial distribution function and the mean-square displacement as a function of time are virtually unaffected by even large energy polydispersity, which is in stark contrast to what happens when size polydispersity is introduced. We here argue -- and validate by simulations of up to 30\% polydispersity -- that this almost invariance of structure and dynamics reflects an approximate invariance of the constant-potential-energy surface. Because $NVU$ dynamics defined as geodesic motion at constant potential energy is equivalent to Newtonian dynamics in the thermodynamic limit, the approximate invariance of the constant-potential-energy surface implies virtually the same physics of energy polydisperse LJ systems as of the standard single-component version. In contrast, the constant-potential-energy surface is significantly affected by introducing size polydispersity.