  We propose and investigate an exactly solvable model of non-equilibrium
Luttinger liquid on a star graph, modeling a multi-terminal quantum wire
junction. The boundary condition at the junction is fixed by an orthogonal
matrix S, which describes the splitting of the electric current among the
leads. The system is driven away from equilibrium by connecting the leads to
heat baths at different temperatures and chemical potentials. The associated
non-equilibrium steady state depends on S and is explicitly constructed. In
this context we develop a non-equilibrium bosonization procedure and compute
some basic correlation functions. Luttinger liquids with general anyon
statistics are considered. The relative momentum distribution away from
equilibrium turns out to be the convolution of equilibrium anyon distributions
at different temperatures. Both the charge and heat transport are studied. The
exact current-current correlation function is derived and the zero-frequency
noise power is determined.
