We show that in the linear response approximation only entropy provides coupling between thermal and electric phenomena. The dissipationless quantum currents — magnetization, superconducting, persistent and topological edge currents — do not produce and transfer entropy and may be excluded from final formulas for thermomagnetic coefficients. The magnetization energy flux, [Formula: see text], in crossed electric and magnetic fields strongly modifies the Poynting vector in magnetic materials and metamaterials, but do not contribute to the heat current. Calculating entropy fluxes of fluctuating Cooper pairs in pure and disordered superconductors, we obtained the fluctuation Nernst coefficient proportional to [Formula: see text] ([Formula: see text] is the Fermi energy). We also introduce the thermomagnetic entropy per unit charge and derive the Nernst coefficient proportional to the difference of the thermoelectric and thermomagnetic entropies. This explains the Sondheimer cancellation and high sensitivity of thermomagnetic phenomena to correlations. In 2D superconductors, the transport entropy transferred by a vortex moving through the background formed by vortex–antivortex pairs is the configuration entropy of [Formula: see text], which strongly exceeds the intrinsic entropy of vortex core. Beyond the linear response, the nonentropic forces can lead to phenomena unexpected from thermodynamics, such as vortex attraction to the moving hot spot. Quantum currents do not transfer entropy and may be used as ideal connectors to quantum nanodetectors.
