Temperature inversion across coexisting phases in two-dimensional driven granular materials

A kinetic temperature difference across coexisting phases is a key feature of the non-equilibrium dynamics observed in granular systems. The evolution of the temperature ratio between the dilute and dense phases across the phase diagram is examined. Building on previous experimental results and recent simulation findings, we report a bimodal distribution of the bond-orientation order parameter in quasi-two-dimensional driven granular materials. Using the trough of P(Ψ6), we categorize particles into two distinct phases and analyze the temperature ratio between them across the phase diagram. Our findings reveal that the order parameter, kinetic energy, and temperature between the dense and dilute phases exhibit nonlinear growth in the density-amplitude phase space. Remarkably, the granular temperature ratio between these phases can either exceed or fall below unity, depending on the specific conditions, similar to phenomena observed in self-propelled particle systems. This behavior is driven by correlated motion with the boundary. Our study thus establishes a direct link between structural order and kinetic motion during phase transitions processes in granular materials.