Influence of temperature correlations on phase dynamics and kinetics of   ultrathin lubricant film
  The melting of ultrathin lubricant film is studied by friction between atomically flat surfaces. The fluctuations of lubricant temperature are taken into account defined by Ornstein-Uhlenbeck process. The phase diagrams and portraits are calculated for the cases of second-order and first-order transitions -- the melting of amorphous and crystalline lubricants. It is shown that in the first case the stick-slip friction domain appears, dividing the regions of dry and sliding friction. In the second case the three stick-slip friction domains arise characterized by transitions between dry, metastable and stable sliding friction. The increase of correlation time of the lubricant temperature fluctuations leads to increasing of the frictional surfaces temperature needed for realization of sliding friction. The singular point, meeting the mode of dry friction, has complex character of stability. The stationary states, corresponding to the stable and metastable sliding friction, are presented by the focus-type singular points. 
A.V.Khomenko