Unifying fluctuation-dissipation temperatures of slow-evolving nonequilibrium systems from the perspective of inherent structures

For nonequilibrium systems, how to define temperature is one of the key and difficult issues to solve. Although effective temperatures have been proposed and studied to this end, it still remains elusive what they actually are. Here, we focus on the fluctuation-dissipation temperatures and report that such effective temperatures of slow-evolving systems represent characteristic temperatures of their equilibrium counterparts. By calculating the fluctuation-dissipation relation of inherent structures, we obtain a temperature-like quantity TIS. For monocomponent crystal-formers, TIS agrees well with the crystallization temperature Tc, while it matches with the onset temperature Ton for glass-formers. It also agrees with effective temperatures of typical nonequilibrium systems, such as aging glasses, quasi-static shear flows, and quasi-static self-propelled flows. From the unique perspective of inherent structures, our study reveals the nature of effective temperatures and the underlying connections between nonequilibrium and equilibrium systems and confirms the equivalence between Ton and Tc.