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We investigate the hydrodynamic regime in metals with momentum-conservingelectron-electron scattering. The conservation of momentum results inwell-defined dynamics whose effects we investigate via the relevant continuityequations. Studying semiclassical thermoelectric transport in the presence of aBerry curvature, we find anomalous contributions to the charge and heattransport currents arising from gradients of the velocity field. Thesecontributions are non-vanishing for systems lacking centro-symmetry, and thecorresponding transport coefficients do not obey the standard Onsagerreciprocity relations. Instead, we show that the response coefficients relatingthe currents to the stress tensor obey independent reciprocity relations withthe stress tensor and thus exhibit cross-tensor effects of the charge densityand the entropy density with the momentum density. The requirement of the lackof centrosymmetry is shown to arise as a consequence of the Curie symmetryprinciple, which prevents cross-tensor effects in isotropic systems.

Vortical currents and reciprocal relations for transport coefficients in the electron hydrodynamic regime