Characteristic temperatures predicted from inherent structures

We calculate the correlation and linear response to external forces for inherent structures (metastable solid states at zero temperature) of different systems. Borrowing the idea of fluctuation-dissipation relation for thermodynamically equilibrated systems, we obtain a temperature-like quantity purely from the correlation and response of inherent structures. For systems with Lennard-Johns, Weeks-Chandler-Andersen, and harmonic particle interactions, we surprisingly find that the temperature-like quantity agrees well with the crystallization or onset temperature for cystal or glass forming liquids. Our study indicates that some equilibrium information can be obtained just from nonequibrium metastable solid states, which thus proposes a novel way to calculate characteristic temperatures. Our results also suggest that effective temperatures previous calculated in ageing glasses may be simply the onset temperature of glass forming liquids.