On a Relation between Fluctuation-Dissipation Theorem and Irreversible Thermodynamics

Abstract

It is first shown that, for some special simple impedances, the stochastic equation describing the fluctuation of macroscopic variables, which is suggested by the fluctuation-dissipation theorem, comes out to be equivalent to the Langevin equation appearing in ordinary irreversible thermodynamics. This does not mean, however, that the ordinary irreversible thermodynamics cannot describe any variables other than those with the simple impedances. It is secondly shown that, on the contrary, any macroscopic variable whose impedance is of the form
Z(iω)=z⁻¹⁄(iω)+z⁰+(iω)z¹+∑_jc_j⁄(iω−p_j),
can be described within the framework of the ordinary irreversible thermodynamics. This is proved by the fact that we can construct, starting from irreversible-thermodynamical equations and using the method of eliminating inner variables, a variable whose impedance is of the above-mentioned form and whose fluctuation-spectrum exactly coincides with that given by the fluctuation-dissipation theorem.