Time dependent current in a nonstationary environment: A microscopic   approach
  Based on a microscopic system reservoir model,where the associated bath is not in thermal equilibrium, we simulate the nonstationary Langevin dynamics and obtained the generalized nonstationary fluctuation dissipation relation (FDR) which asymptotically reduces to the traditional form. Our Langevin dynamics incorporates non-Markovian process also, the origin of which lies on the decaying term of the nonstationary FDR. We then follow the stochastic dynamics of the Langevin particle based on the Fokker-Planck-Smoluchowski description, in ratchet potential to obtain the steady and time dependent current in an analytic form. We also examine the influence of initial excitation and subsequent relaxation of bath modes on the transport of the Langevin particle to show that the nonequilibrium nature of the bath leads to both strong non-exponential dynamics as well as nonstationary current. 
Satyabrata Bhattacharya, Suman Kumar Banik, Sudip Chattopadhyay,   Jyotipratim Ray Chaudhuri