AbstractA kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice of 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 of transport, q*. for a single vacancy jump of the impurity, q* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms involving time correlation functions. The most important non-equilibrium term concerns the correlation between the force on the impurity 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
Non-equilibrium coherence dynamics in one-dimensional Bose gases