Non-Isothermal Fluctuation-Dissipation Relations and Brownian   Thermometry
  The classical theory of Brownian motion rests on fundamental laws of statistical mechanics, such as the equipartition theorem and the fluctuation-dissipation theorem, which are not applicable in non-isothermal situations. We derive the generalized fluctuation-dissipation relations and Langevin equations governing such non-isothermal Brownian motion, including explicit results for the frequency-dependent noise temperature and Brownian thermometry far from equilibrium. 
Gianmaria Falasco, Manuel Victor Gnann, Klaus Kroy
cond-mat.stat-mech