  Nonequilibrium situations where selected currents are suppressed are of
interest in fields like thermoelectrics and spintronics, raising the question
of how the related noises behave. We study such zero-current charge, spin, and
heat noises in a two-terminal mesoscopic conductor. In the presence of voltage,
spin and temperature biases, the nonequilibrium (shot) noises of charge, spin,
and heat can be arbitrarily large, even if their average currents vanish.
However, as soon as a temperature bias is present, additional equilibrium
(thermal-like) noise necessarily occurs. We show that this equilibrium noise
sets an upper bound on the zero-current charge and spin shot noises, even if
additional voltage or spin biases are present. We demonstrate that these bounds
can be overcome for heat transport by breaking the spin and electron-hole
symmetries, respectively. By contrast, we show that the bound on the charge
noise for strictly two-terminal conductors even extends into the
finite-frequency regime.
