Nonequlibrium phase transition of an open Takayama-Lin Liu-Maki chain coupled with two reservoirs is investigated.
We will demonstrate destructive and constructive roles of a current.

As a destructive role, we discuss how the orders parameter behaves when system is driven by either a voltage or a current.
When the bias voltage is chosen to be a control parameter, the phase transition between ordered and normal phases is found to be first or second order. Then, the voltage-current characteristics is S-shaped in some parameter region. In contrast, when the current is chosen to be a control parameter, all the non-trivial solutions of the self-consistent equation are found to become stable. In this case, the phase transition between the ordered and normal phases is always second order and negative differential conductivity appears at low temperature.

As a constructive role, we discuss a formation of polaron due to the current.
This polaron formation is a genuine nonequilibrium phenomenon, as there is a lower threshold current below which they cannot exist. It is considered to be an example of microscopic dissipative structure.