Abstract
A derivation of the fluctuation-dissipation (FD) theorem for the frequency-dependent specific heat of a system described by a master equation is presented. The FD theorem is illustrated by a number of simple examples, 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 cutoffs---a collection of two-level systems and a system described by the energy master equation---the frequency-dependent specific heat in dimensionless units becomes universal at low temperatures, i.e., independent of both energy distribution and temperature. These two models give almost the same universal frequency-dependent specific heat, which compares favorably to experiments on supercooled alcohols. \textcopyright{} 1996 The American Physical Society.
Highlights
Ac calorimetry was introduced in the 1960’s as an accurate method for measuring the ordinary dc specific heat.[1,2]
The FD theorem is illustrated by a number of simple examples, 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 cutoffs—a collection of two-level systems and a system described by the energy master equation—the frequency-dependent specific heat in dimensionless units becomes universal at low temperatures, i.e., independent of both energy distribution and temperature
Summary
A derivation of the fluctuation-dissipationFDtheorem for the frequency-dependent specific heat of a system described by a master equation is presented. It is shown that for two quite different models with low-energy cutoffs—a collection of two-level systems and a system described by the energy master equation—the frequency-dependent specific heat in dimensionless units becomes universal at low temperatures, i.e., independent of both energy distribution and temperature. These two models give almost the same universal frequencydependent specific heat, which compares favorably to experiments on supercooled alcohols. These two models give almost the same universal frequencydependent specific heat, which compares favorably to experiments on supercooled alcohols. ͓S0163-1829͑96͒06446-6͔
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