  We investigate the particle and heat transport in quantum junctions with the
geometry of star graphs. The system is in a nonequilibrium steady state,
characterized by the different temperatures and chemical potentials of the heat
reservoirs connected to the edges of the graph. We explore the
Landauer-Buettiker state and its orbit under parity and time reversal
transformations. Both particle number and total energy are conserved in these
states. However the heat and chemical potential energy are in general not
separately conserved, which gives origin to a basic process of energy
transmutation among them. We study both directions of this process in detail,
introducing appropriate efficiency coefficients. For scale invariant
interactions in the junction our results are exact and explicit. They cover the
whole parameter space and take into account all nonlinear effects. The energy
transmutation depends on the particle statistics.
