Equilibrium States Corresponding to Targeted Nonequilibrium Pair Statistics

Nonequilibrium many-body systems are ubiquitous in physical, chemical and biological phenomena. Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)] recently conjectured that any realizable pair correlation function $g_2({\bf r})$ or structure factor $S({\bf k})$ corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble at positive temperature $T$ involving only (up to) effective pair interactions. To test this conjecture, we apply a new inverse methodology for two different nonequilibrium 2D models: the nonhyperuniform random sequential addition (RSA) process and a hyperuniform "perfect glass". We show that these nonequilibrium systems

are indeed achievable by equilibrium many-body systems at positive temperature involving up to two-body potentials. We also demonstrate that unlike typical liquids (e.g. high-density Lennard-Jones fluids), both of these equilibrium systems exhibit highly disordered inherent structures upon quenching. Our findings provide further support to the Zhang-Torquato conjecture and demonstrate the capability of equilibrium systems to realize properties conventionally associated with nonequilibrium systems.