Spin currents in thermodynamic equilibrium?

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The standard definition of a spin current, applied to the conductors lacking inversion symmetry, results in nonzero spin currents. I demonstrate that the spin currents do not vanish even in the thermodynamic equilibrium, in the absence of external fields. These currents are dissipationless and are not associated with a real spin transport. The result should be taken as a warning indicating problems inherent in the theory of transport spin currents driven by external fields.
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