Non-equilibrium systems are less understood compared to their equilibriumcounter-parts. I will introduce a simple non equilibrium model which isexactly solvable and explain it’s application to Celebrity Markets(crickets performance), Biological systems, Generic rules fornon-equilibrium transitions, Anomalous diffusion etc.

We discuss a Polyakov loop enhanced NJL model to describe the QCD phase transition. Linear and nonlinear susceptibilities, specific heat, speed of sound etc. have been obtained and compared to those obtained through Lattice regularization.