For equilibrium/ground state systems, a (Wilson) renormalization group transformation
produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such that long-wave/asymptotic behaviour of $H_{\Lambda}$
is the same as of $H_{\Lambda'}$ after rescaling by $\Lambda/\Lambda'$.
The idea of this definition implies an exact starting point for RG formalisms,
with technical details varying between the fields and approximation methods.
(For examples, see arXiv:1012.5604 and Wikipedia article).

Now, for **non-equilibrium condensed-matter systems** there is research direction aiming
at generalization of the RG approach to a steady state, e.g., a voltage-biased strongly interacting quatum dot (or Kondo impuryity). For examples, see arXiv:0902.1446 and related references.

I would like to understand the conceptional foundations for the non-equlibrium RG.

What is the definition of an RG transofrmation in a non-equilibirum,
steady state ensemble?

I see a problem in the fact that the non-equilibirum desnity matrix which is used to define
the problem is not a function of the Hamiltonian alone, thus it is not clear to me how
is the effect of the change in the cut-off is split between the Hamiltonian
(running couplings) and the density matrix (renormaltizaton of the boundary/external conditions?)

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