  A long time ago F. Bloch showed that in a system of interacting
non-relativistic particles the net particle-number current must vanish in any
equilibrium state. Bloch's argument does not generalize easily to the energy
current. We devise an alternative argument which proves the vanishing of the
net energy currents in equilibrium states of lattice systems as well as systems
of non-relativistic particles with finite-range potential interactions. We
discuss some applications of these results. In particular, we show that neither
a 1d lattice system nor a 1d system of non-relativistic particles with
finite-range potential interactions can flow to a Conformal Field Theory with
unequal left-moving and right-moving central charges.
