Entropy, dynamics, and instantaneous normal modes in a random energy model
It is shown that the fraction f(u) of imaginary-frequency instantaneous normal modes (INM) may be defined and calculated in a random energy model (REM) of liquids. The configurational entropy S(c) and the averaged hopping rate among the states, R, are also obtained and related to f(u) with the results R approximately f(u) and S(c)=a+b ln(f(u)). The proportionality between R and f(u) is the basis of existing INM theories of diffusion, so the REM further confirms their validity. A link to S(c) opens new avenues for introducing INM into dynamical theories. Liquid states are usually defined by assigning a configuration to the minimum to which it will drain, but the REM naturally treats saddle barriers on the same footing as minima, which may be a better mapping of the continuum of configurations to discrete states. Requirements for a detailed REM description of liquids are discussed.
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Chemistry Department, Boston University, Boston, Massachusetts 02215, USA.