Statefinder Diagnostic for Quintessence with or without Thermal   Interaction
  The cosmological dynamics of minimally coupled scalar field that couples to the background matter with thermal interactions is investigated by using statefinder diagnostics. The time evolution of the statefinder pairs $\{r,s\}$ and $\{r,q\}$ are obtained under the circumstance that different values of model parameters are chosen. We show that the thermal coupling term does not affect the location of the late-time attractor, but exert an influence on the evolution of the statefinder parameters. The most notable feature of the $r-s$ plane for the thermal coupling model which is distinguished from the other dark energy models is that some part of the curve with thermal coupling can form a closed loop in the second quadrant ($r>1,s<0$). 
Wei-Zhong Liu, Dao-Jun Liu