  Quantum Renyi relative entropies provide a one-parameter family of distances
between density matrices, which generalizes the relative entropy and the
fidelity. We study these measures for renormalization group flows in quantum
field theory. We derive explicit expressions in free field theory based on the
real time approach. Using monotonicity properties, we obtain new inequalities
that need to be satisfied by consistent renormalization group trajectories in
field theory. These inequalities play the role of a second law of
thermodynamics, in the context of renormalization group flows. Finally, we
apply these results to a tractable Kondo model, where we evaluate the Renyi
relative entropies explicitly. An outcome of this is that Anderson's
orthogonality catastrophe can be avoided by working on a Cauchy surface that
approaches the light-cone.
