FLUCTUATION-DISSIPATION THEOREM FOR FREQUENCY-DEPENDENT SPECIFIC-HEAT

A derivation of the fluctuation-dissipation (FD) theorem for the frequ ency-dependent specific heat of a system described by a master equatio n is presented. The FD theorem is illustrated by a number of simple ex amples, including a system described by a linear Langevin equation, a two-level system, and a system described by the energy master equation . It is shown that for two quite different models with low-energy cuto ffs-a collection of two-level systems and a system described by the en ergy master equation-the frequency-dependent specific heat in dimensio nless units becomes universal at low temperatures, i.e., independent o f both energy distribution and temperature. These two models give almo st the same universal frequency-dependent specific heat, which compare s favorably to experiments on supercooled alcohols.