Statistical Mechanics of Thermotransport of a Heavy Impurity in an Insulating Solid *

A kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice o f lighter atoms in a temperature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jump probability and hence the heat o f transport, q*, for a single vacancy jump o f the impurity. <7* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms in­ volving tim e correlation functions. The m ost important non-equilibrium term concerns the cor­ relation between the force on the im purity and a microscopic heat flux. A plausible extension to three dimensions is suggested and the relation to earlier isothermal and non-isothermal theories is indicated.