Non-equilibrium Statistical Physics with fictitious time
Problems in non-equilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. In nature, thermal equilibrium is rather an exception than a rule. There are various models of non-equilibrium statistical mechanics that do not evolve towards equilibrium. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia and Rose. We show that instead of using response field, one can follow the stochastic quantization of Parisi and Wu, by introducing a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in non-equilibrium statistical physics.